A multiple-choice quiz
by xxharryxx.
Estimated time: 5 mins.

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Quiz Answer Key and Fun Facts

Answer:
**16 **

Set up a formula: s^2 = 256. To get s alone, find the square root of both sides of the equation. The square root of s^2 is s, and the square root of 256 is 16. A side's length is equal to sixteen inches.

Set up a formula: s^2 = 256. To get s alone, find the square root of both sides of the equation. The square root of s^2 is s, and the square root of 256 is 16. A side's length is equal to sixteen inches.

Answer:
**6*sqrt2**

First, set up your formula: 2*sqrt2 * L = 24. You know that L has to be x*sqrt2 because the answer has no radicals and to make a sqrt2 a whole number, you must multiply by sqrt2. sqrt2 and sqrt2 make 2 when multiplied together, so you now have 2 * x * 2 = 24 as your new equation.

It is now easy to solve: 4x=24. Divide both sides by four to get x=6. x is attached to sqrt2, so your length is 6*sqrt2 inches.

First, set up your formula: 2*sqrt2 * L = 24. You know that L has to be x*sqrt2 because the answer has no radicals and to make a sqrt2 a whole number, you must multiply by sqrt2. sqrt2 and sqrt2 make 2 when multiplied together, so you now have 2 * x * 2 = 24 as your new equation.

It is now easy to solve: 4x=24. Divide both sides by four to get x=6. x is attached to sqrt2, so your length is 6*sqrt2 inches.

Answer:
**7 **

There are several ways of going about this problem. One is to punch 52 into your calculator and push the square root button to see that it approximately equals 7.211, which is pretty close to seven. You can also simplify your sqrt52 to 2*sqrt13. Do this by finding the prime factorization of 52, 2*2*13. You have 2 sqrt2's that cancel to two.

Then find the square root of 13 using a calculator and multiply it by 2. You'll get about 7.211, which is close to seven. If you have perfect squares memorized, you'll know that 49 and 64 are perfect squares. 52 is closer to 49, the square of seven.

There are several ways of going about this problem. One is to punch 52 into your calculator and push the square root button to see that it approximately equals 7.211, which is pretty close to seven. You can also simplify your sqrt52 to 2*sqrt13. Do this by finding the prime factorization of 52, 2*2*13. You have 2 sqrt2's that cancel to two.

Then find the square root of 13 using a calculator and multiply it by 2. You'll get about 7.211, which is close to seven. If you have perfect squares memorized, you'll know that 49 and 64 are perfect squares. 52 is closer to 49, the square of seven.

Answer:
**3*sqrt2**

First, set up your formula: 2(12*sqrt2) + 2W = 30*sqrt2. Simplify your 2(12*sqrt2) to 24*sqrt2, and then subtract 24*sqrt2 from both sides to get 2W = 6*sqrt2. Divide both sides by two to find that the width is equal to 3*sqrt2.

First, set up your formula: 2(12*sqrt2) + 2W = 30*sqrt2. Simplify your 2(12*sqrt2) to 24*sqrt2, and then subtract 24*sqrt2 from both sides to get 2W = 6*sqrt2. Divide both sides by two to find that the width is equal to 3*sqrt2.

Answer:
**2 **

First, set up your formula to find the diagonal's length: 2(1^2) = c^2. It simplifies to 2 = c^2. Find the square root of both sides to get c alone. The square root of two can simply be expressed as sqrt2, and the square root of c^2 is equal to c. You then make a square using the diagonal of length sqrt2 as a side.

The side length of the square will be sqrt2. You can then use the formula s^2 to find the area. (sqrt2)^2 = sqrt2 * sqrt2 = 2.

First, set up your formula to find the diagonal's length: 2(1^2) = c^2. It simplifies to 2 = c^2. Find the square root of both sides to get c alone. The square root of two can simply be expressed as sqrt2, and the square root of c^2 is equal to c. You then make a square using the diagonal of length sqrt2 as a side.

The side length of the square will be sqrt2. You can then use the formula s^2 to find the area. (sqrt2)^2 = sqrt2 * sqrt2 = 2.

Answer:
**48**

Plug your data into the formula: (8*sqrt3)(4*sqrt3)/2. Simplify by multiplying whole numbers and radicals together. You now have (32*3)/2, which can be simplified to 96/2, and then to 48 square units.

Plug your data into the formula: (8*sqrt3)(4*sqrt3)/2. Simplify by multiplying whole numbers and radicals together. You now have (32*3)/2, which can be simplified to 96/2, and then to 48 square units.

Answer:
**200**

The length of the first square's sides is 6*sqrt5 inches. Find the area by plugging 6*sqrt5 into the formula for a square's area: (6*sqrt5)^2. Square 6 to get 36. Square sqrt5 to get 5. Multiply 36 and 5 to get 180 square inches in the area of the square.

The second square has a side length that is one-third of 6*sqrt5, which is 2*sqrt5. Square it to find the area. Square 2 to get 4 and square sqrt5 to get 5. Multiply them to get 20 square inches as the area of the second square. Add 180 and 20 together to get 200 square inches in the combined area of the squares.

The length of the first square's sides is 6*sqrt5 inches. Find the area by plugging 6*sqrt5 into the formula for a square's area: (6*sqrt5)^2. Square 6 to get 36. Square sqrt5 to get 5. Multiply 36 and 5 to get 180 square inches in the area of the square.

The second square has a side length that is one-third of 6*sqrt5, which is 2*sqrt5. Square it to find the area. Square 2 to get 4 and square sqrt5 to get 5. Multiply them to get 20 square inches as the area of the second square. Add 180 and 20 together to get 200 square inches in the combined area of the squares.

Answer:
**4*sqrt5**

Plug your numbers into the formula: 4^2 + 8^2 = c^2. Simplify to 16 + 64 = c^2, and then to 80 = c^2. Find the square root of both sides to get c alone. The square root of c^2 is c, and the square root of 80 is found by finding the prime factorization, which is 2 * 2 * 2 * 2 * 5. You have two pairs of twos. Each pair multiplies to two, which means you can multiply them to get 4. You have 4 and sqrt5 left, which means c is equal to 4*sqrt5 units.

Plug your numbers into the formula: 4^2 + 8^2 = c^2. Simplify to 16 + 64 = c^2, and then to 80 = c^2. Find the square root of both sides to get c alone. The square root of c^2 is c, and the square root of 80 is found by finding the prime factorization, which is 2 * 2 * 2 * 2 * 5. You have two pairs of twos. Each pair multiplies to two, which means you can multiply them to get 4. You have 4 and sqrt5 left, which means c is equal to 4*sqrt5 units.

Answer:
**63*pi**

The radius is equal to one-half the length of the diameter. Divide 6*sqrt7 by 2 to get 3*sqrt7, the circle's radius. Plug it in the formula to find the area of the circle: (3*sqrt7)^2. Square 3 to get 9 and sqrt7 to get 7. Then, multiply them together to get 63. You then would multiply by pi, but this problem asks for the answer in terms of pi, so your answer is 63*pi.

The radius is equal to one-half the length of the diameter. Divide 6*sqrt7 by 2 to get 3*sqrt7, the circle's radius. Plug it in the formula to find the area of the circle: (3*sqrt7)^2. Square 3 to get 9 and sqrt7 to get 7. Then, multiply them together to get 63. You then would multiply by pi, but this problem asks for the answer in terms of pi, so your answer is 63*pi.

Answer:
**4*sqrt3**

Let x equal the side length of a cube. The diagonal of a cube can be expressed as x^2 + (x*sqrt2)^2, where x is the length of a side and x*sqrt2 is the length of a face diagonal. To prove that x*sqrt2 is the length of a face diagonal, use the Pythagorean Theorem. x^2 + x^2 = c^2. 2*x^2 = c^2. Find the square root of both sides.

The square root of c^2 is c, and the square root of 2*x^2 is x*sqrt2. c = x*sqrt2. Now, use the Pythagorean Theorem to find the length of one side of the cube. x^2 + (x*sqrt2)^2 = 12^2. Simplify to x^2 + 2*x^2 = 144, and then to 3*x^2 = 144. Divide each side by three to get x^2 = 48, and then find the square root of both sides.

The square root of x^2 is x, and the square root of 48 can be determined by its prime factorization: 2*2*2*2*3.

There are two pairs of 2's that both multiply to 2. Together, they make 4, and you have sqrt3 left over. The length of one side of the cube is 4*sqrt3 centimeters.

Let x equal the side length of a cube. The diagonal of a cube can be expressed as x^2 + (x*sqrt2)^2, where x is the length of a side and x*sqrt2 is the length of a face diagonal. To prove that x*sqrt2 is the length of a face diagonal, use the Pythagorean Theorem. x^2 + x^2 = c^2. 2*x^2 = c^2. Find the square root of both sides.

The square root of c^2 is c, and the square root of 2*x^2 is x*sqrt2. c = x*sqrt2. Now, use the Pythagorean Theorem to find the length of one side of the cube. x^2 + (x*sqrt2)^2 = 12^2. Simplify to x^2 + 2*x^2 = 144, and then to 3*x^2 = 144. Divide each side by three to get x^2 = 48, and then find the square root of both sides.

The square root of x^2 is x, and the square root of 48 can be determined by its prime factorization: 2*2*2*2*3.

There are two pairs of 2's that both multiply to 2. Together, they make 4, and you have sqrt3 left over. The length of one side of the cube is 4*sqrt3 centimeters.

This quiz was reviewed by FunTrivia editor crisw before going online.

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