Question

Alexander was solving maths without any calculator. He needs to find the decimal value of $\sqrt{10}$ up to two decimal places. Help Alexander by finding the approximate value of $\sqrt{10}$ upto two decimal place.

• A. $3$
• B. $3.16$
• C. $3.17$
• D. $4$

Answer 1

The correct option is B $3.16$

Let's use the perfect square method.

The largest perfect square smaller than $10$ is $9.$

And, the smallest perfect square larger than $10$ is $16.$

$\therefore 9<10<16$
(taking square root throughout the inequality)
$\Rightarrow \sqrt{9}<\sqrt{10}<\sqrt{16}$
$\Rightarrow 3<\sqrt{10}<4$
$\therefore \sqrt{10}=3.\underset{–}{}$

For two decimal place digits, consider $100,000.$

The largest perfect square smaller than $100,000$ is ${316}^2.$

And, the smallest perfect square larger than $100,000$ is ${317}^2.$

$\therefore {316}^2<100,000<{317}^2$
(dividing $10,000$ throughout the inequality)
$\therefore \frac{{316}^2}{{100}^2}<\frac{100000}{{100}^2}<\frac{{317}^2}{{100}^2}$
(taking square root throughout the inequality)
$\Rightarrow \sqrt{\frac{{316}^2}{{100}^2}}<\sqrt{10}<\sqrt{\frac{{317}^2}{{100}^2}}$
$\Rightarrow \frac{316}{100}<\sqrt{10}<\frac{317}{100}$
$\Rightarrow 3.16<\sqrt{10}<3.17$
$\therefore \sqrt{10}=3.\underset{–}{16}$

The decimal form of $\sqrt{1}0$ up to two decimal places is $\mathrm{3.16.}$