Question

If √2916​=54, what is the value of √29.16​+√0.2916​+√0.002916​+√0.00002916​

Answer 1

Answer:

As there are two square roots, which one are you referring to? I’m positively in favour of one root; whereas I have negative feelings towards the other!

My bad, I misunderstood; you actually want me to show you how to calculate the roots.

This is something that is actually quite easy to do in your head! But, I’ll make it easier for you.

I’ll start with the positive square root:

0.2916−−−−−√=291610,000−−−−−√=2916√10,000√=2916√100

As 2,916 is clearly a multiple of 4 (2,916=29×100+16=29×4×25+4×4) , we can thus rewrite the expression as:

4×729√100=2729√100

Let’s look at the digit sum of 729: 7 + 2 + 9 = 18; as 18 is clearly a multiple of 9, so is 729 thus we can rewrite the expression as:

29×81√100=681√100

Well, you should know that the principal square root of 81 is 9, thus your expression becomes:

6×9100=54100=0.54

What about the second square root? Simple, its just - 0.54

Answer: ±0.54

Answer 2

$\huge \bold{answer}$

$\small { \sqrt{29.16} + \sqrt{0.2916} + \sqrt{0.002916} + \sqrt{0.00002916}}$
$= > \sqrt{ \frac{2916}{ {10}^{2} } } + \sqrt{ \frac{2916}{ {10}^{4} } } + \sqrt{ \frac{2916}{ {10}^{6} } } + \sqrt{ \frac{2916}{ {10}^{8} } }$
$= > \frac{54}{10} + \frac{54}{100} + \frac{54}{1000} + \frac{54}{10000}$
$= > 5.4 + 0.54 + 0.054 + 0.0054$
$= > 5.9994$
$\therefore\sqrt{2916} + \sqrt{0.02916} + \sqrt{0.002916} + 0.00002916$
$\boxed{ = 5.9994}$