Question

Using the ratio of perfect squares method, what is square root of 112 rounded to the nearest hundredth?

Answer 1

To find the square root of 112 using the ratio of perfect squares method, we can use the formula x = (a + (b-a) * sqrt(n-a^2))/(b-a), where a is the lower perfect square, b is the higher perfect square, and n is the number we want to find the square root of. Plugging in the values, we can evaluate the formula to get an approximation of the square root of 112.

Step-by-step explanation:

To find the square root of 112 using the ratio of perfect squares method, we need to find two perfect squares that surround 112. The perfect squares closest to 112 are 100 and 121. The square root of 100 is 10, and the square root of 121 is 11. Since 112 is between 100 and 121, the square root of 112 is between 10 and 11.

To find a more accurate approximation, we can use the formula:

x = (a + (b-a) * sqrt(n-a^2))/(b-a)

where a is the lower perfect square (100), b is the higher perfect square (121), and n is the number we want to find the square root of (112). Plugging in the values, we get:

x = (10 + (112-100) * sqrt(112-100))/(121-100) = (10 + 12 * sqrt(12))/(21)

This cannot be simplified further, so we can use a calculator to evaluate it to get an approximation of the square root of 112.

Answer 2

First, you have to think of any perfect squares that multiply to 112. The only ones I can think of are 16 and 7. So now you have the square root of 16 * 7. Now you can reduce the 16 because the square root of 16 is 4. So the answer is 4 times the square root of 7.