Question

The square root of (2011)5 is
​

Answer 1

Answer:

100

Step-by-step explanation:

Answer 2

$\sf The \: square \: root \: of \: \: (2011)_5 = (31)_5$

Given :

The number

$\sf (2011)_5$

To find :

The square root of the number

Solution :

Step 1 of 3 :

Express in decimal

$\sf (2011)_5$

$\sf = (2 \times {5}^{3} + 0 \times {5}^{2} + 1 \times {5}^{1} + 1 \times {5}^{0} )$

$\sf = 250 + 0 + 5 + 1$

$\sf = 256$

Step 2 of 3 :

Find the square root of the number

The square root of 256

$\sf = \sqrt{256}$

$\sf = 16$

Step 3 of 3 :

Express with respect to base 5

The required square root

$\sf =(16)_{10}$

$\sf =(31)_5$

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