Estimating Roots of Irrational Numbers

Which is the best estimate of the square root of 63?

• 7.1

• 7.3

• 7.5

• 7.9

Between which two whole numbers does the √115 fall?

• 9 and 10

• 10 and 11

• 9 and 11

• 11 and 12

• A
• B
• C
• D

Which point best represents √47?

• A

• D

• E

• F

√89

• 9.4

• 9.6

• 9

• 44.5

What is the approximate value of √28 ?

• 5.6

• 5.9

• 5.3

• 8

Answer explanation

 $25<28<36$     *closer to 25
 $\sqrt{25}<\sqrt{28}<\sqrt{36}$      *closer to  $\sqrt{25}$  
 $5<\sqrt{28}<6$      *closer to 5

 $\sqrt{28}\approx5.3$      *Closest option provided to 5

Estimate the value of √7 to the nearest whole number.

• 3

• 4

• 2

• 1

The √98 falls between what two numbers on a number line?

• 10 and 11

• 11 and 12

• 9 and 10

• 90 and 100

Answer explanation

98 is between perfect squares 81 and 100.
$81<98<100$

This means the square root of 98 is between the square roots of those numbers.
$\sqrt{81}<\sqrt{98}<\sqrt{100}$

$9<\sqrt{98}<10$

√14

• 4

• 3.2

• 3.8

• 7

Estimate the square root as a decimal to the nearest tenth.