If $$\sqrt{506.25} = 22.5$$​, then what is the value of  $$\sqrt{0.00050625}$$​?

Correct option is C

Given:
​$$\sqrt{506.25} = 22.5$$​​
Formula Used:
Properties of square roots: $$\sqrt{a × 10^{-n}} = \sqrt{a} × 10^{-\frac{n}{2}}$$​​
Solution:
We need to find the value of  $$\sqrt{0.00050625}$$​​
Notice that the decimal point in 0.00050625 has been shifted 6 places to the left compared to 506.25.
We can express the target number as follows.
0.00050625 = $$506.25 × 10^{-6}$$​​
Take the square root on both sides.
​$$\sqrt{0.00050625} = \sqrt{506.25 × 10^{-6}}$$​​ $$= \sqrt{506.25} × \sqrt{10^{-6}}$$​​
Substitute the given value $$\sqrt{506.25} = 22.5.$$​​
​$$= 22.5 × 10^{-3}$$​​
= 0.0225
Final Answer
So the correct answer is (c)