Question

☯︎ǫᴜᴇsᴛɪᴏɴ

Simplify:-
$\sqrt{0.2209} + \sqrt{0.1681} \\ \sqrt{0.2209 - \sqrt{0.1681} }$

Nᴏ sᴘᴀᴍ ᴘʟᴢ​

Answer 1

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,

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

And,

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

Therefore,

$\color{green}\sf\sqrt{2209}+\sqrt{22.09}+\sqrt{0.2209}$