Question

What is the square root of 0.49?

Answer 1

Hint: To find the square root of 0.49, we have to first convert this decimal value into its fractional form. Then, we have to take the square root of this result. We have to apply the property of roots, that is, \[\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\] . Then, we have to take the square root of the values. If the result is in fractional form, we have to convert it into decimal.

Complete step-by-step answer:
We have to find the square root of 0.49. Let us write 0.49 in terms of fraction. We know that the decimal part has a hundredth place. So, we will divide 49 by 100 because the result of this division will be 0.49.
$\Rightarrow 0.49=\dfrac{49}{100}$
Now, we have to take the square root of this value.
$\Rightarrow \sqrt{0.49}=\sqrt{\dfrac{49}{100}}$
We know that \[\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\] . Hence, we can write the above value as
$\Rightarrow \sqrt{\dfrac{49}{100}}=\dfrac{\sqrt{49}}{\sqrt{100}}$
Now, we have to write the roots of these numbers. We know that 49 and 100 are perfect squares, that is, ${{7}^{2}}=49$ and ${{10}^{2}}=100$ . Therefore, the result of the above operations is
$\Rightarrow \dfrac{\sqrt{49}}{\sqrt{100}}=\dfrac{7}{10}$
Now, we have to convert the fractional; result into its decimal form.
$\Rightarrow \dfrac{7}{10}=0.7$
Hence, the square root of 0.49 is 0.7.

Note: Students must know how to convert a decimal number into its fractional form. They must also know the perfect squares of numbers. In this question, the decimal part of 0.49 is a perfect square. Therefore, we need not apply the division method to find the square root.