Estimating Square Roots

The video tutorial explains a method to estimate the square root of a number without using a calculator. It begins by identifying the perfect squares between which the number lies, in this case, 28 is between 25 and 36. Since 28 is closer to 25, the approximation starts with 5 plus a fraction. The fraction's denominator is the product of 2 and the square root of 25, while the numerator is the difference between 28 and 25. Simplifying gives an approximation of 5.3, which is close to the calculator value.

What is the first step in estimating a square root without a calculator?

• Use a calculator to find the exact square root.

• Find the two perfect squares between which the number lies.

• Estimate the square root by guessing.

• Multiply the number by itself.

Which two perfect squares is the number 28 between?

• 36 and 49

• 16 and 25

• 25 and 36

• 9 and 16

How do you form the denominator of the fraction used in the approximation?

• By multiplying two by the square root of the closer perfect square.

• By subtracting the smaller perfect square from the larger one.

• By dividing the number by two.

• By adding the two perfect squares.

What is the numerator of the fraction in the approximation process?

• The product of the radicands of 25 and 28.

• The difference between the radicands of 28 and 25.

• The sum of the radicands of 25 and 28.

• The difference between the radicands of 28 and 36.

What is the approximate square root of 28 using this method?

• 5.7

• 5.3

• 5.5

• 6.0