Question
Find the square root of:
$2\frac{137}{196}$
$2\frac{137}{196}$
✓
Answer
We know,
$\sqrt{2\frac{137}{196}}=\sqrt{\frac{529}{196}}=\frac{\sqrt{529}}{\sqrt{196}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{529}=\sqrt{23\times23}=23$
$\sqrt{196}=\sqrt{2\times2\times7\times7}=2\times7=14$
$\therefore\sqrt{2\frac{137}{196}}=\frac{23}{14}$
$\sqrt{2\frac{137}{196}}=\sqrt{\frac{529}{196}}=\frac{\sqrt{529}}{\sqrt{196}}$
Now, let us compute the square roots of the numerator and the denominator separately.
$\sqrt{529}=\sqrt{23\times23}=23$
$\sqrt{196}=\sqrt{2\times2\times7\times7}=2\times7=14$
$\therefore\sqrt{2\frac{137}{196}}=\frac{23}{14}$
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