Question

Evaluate √2209 , then find the value of √2209 + √22.09 + √0.2209

Answer 1

Step-by-step explanation:

root 2209= 47

=root2209+root22.09+root0.2209

=47+4.7+0.47

=52.17

Answer 2

√2209 = 47

√2209 + √22.09 + √0.2209 = 52.17

Step-by-step explanation:

$\sqrt{2209}$

If we pair the numbers

$\sqrt{\bar{22}\bar{09}}$

Now we need to find a number whose square is less than the first pair, the first pair is 22

If we take 4, then 4² = 16, and 16 < 22

Since the last digit is 9 therefore, the last digit can either be 3 or 7

Therefore, the square root can be either 43 or 47

If we take 43 then we find that 43 × 43 = 1849, which is not out number

If we take 47 then 47 × 47 = 2209

Therefore,

$\sqrt{2209}=47$

Now,

$\sqrt{22.09}=\sqrt{\frac{2209}{100}}=\frac{\sqrt{2209}}{\sqrt{100}}=\frac{47}{10}=4.7$

And,

$\sqrt{0.2209}=\sqrt{\frac{2209}{10000}}=\frac{\sqrt{2209}}{\sqrt{10000}}=\frac{47}{100}=0.47$

Therefore,

$\sqrt{2209}+\sqrt{22.09}+\sqrt{0.2209}$

$=47+4.7+0.47$

$=52.17$

Hope this answer is helpful.

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