Question

approximate each irrational number to the nearest hundredth without using a calculator square root of 118 and 319​

Answer 1

Answer:

$\sqrt{118}\approx 10.86$

$\sqrt{319}\approx 17.86$

Step-by-step explanation:

Consider the provided number.

We need to find the approximate value of $\sqrt{118}$ to the nearest hundredth.

First find two perfect squares that the irrational number falls between.

$100$

118 is lying between 100 and 121, therefore the square root value of 118 will be somewhere between 10 and 11.

$\sqrt{100}$

$10$

118 is closer to 121 as compare to 100.

Therefore, $\sqrt{118}\approx 10.86$

Consider the number $\sqrt{319}$

First find two perfect squares that the irrational number falls between.

$289$

319 is lying between 289 and 324, therefore the square root value of 319 will be somewhere between 17 and 18.

$\sqrt{289}$

$17$

319 is closer to 324 as compare to 289.

Therefore, $\sqrt{319}\approx 17.86$