√(1183)/√(2023) = √(1183/2023) = √(1183 ÷ 7/2023 ÷ 7) lt;br/ gt; = √(169/289) = √(13 × 13/17 × 17) = 13/17 ...

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Finding Square Root through Prime Factorisation

Evaluate: √11...

Question

Evaluate: $\frac{\sqrt{1183}}{\sqrt{2023}}$

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Solution

Factorise:
$1183 = 7 \times 13 \times 13$
$2023 = 7 \times 17 \times 17$

$\frac{\sqrt{1183}}{\sqrt{2023}} = \sqrt{\frac{7 \times 13 \times 13}{7 \times 17 \times 17}}$
$= \sqrt{\frac{13 \times 13}{17 \times 17}}$
$= \frac{13}{17}$

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