Question

simplify 3√45-√125+√200-√50 solve this question​

Answer 1

Answer:

9√5 - 5√5 + 10√2 - 5√2 = 4√5 + 5√2

Hope it helps.

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Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

As, we have to find the value of

$\sf{3\sqrt{45} - \sqrt{125} + \sqrt{200} - \sqrt{60}}$

So, we will make factors of 45, 125, 200 and 50.

$\sf{\small{→ 3 \sqrt{3 \times 3 \times 5} - \sqrt{5 \times 5 \times 5} + \sqrt{2 \times 2 \times 2 \times 5 \times 5} - \sqrt{2 \times 5 \times 5}}} \\ \\ \sf{→ 9\sqrt{5} - 5 \sqrt{5} + 10\sqrt{2} - 5\sqrt{2}} \\ \\ \sf{→ 4\sqrt{5} + 5\sqrt{2}}$

$\rule{200}{2}$

Prime factorisation of 45

$\begin{array}{r | l} 3 & 45 \\ \cline{1-2} 3 & 15 \\ \cline{1-2} 5 & 5 \\ \cline{1-2} & 1 \end{array}$

$\rule{200}{2}$

Prime factorisation of 125

$\begin{array}{r | l} 5 & 125 \\ \cline{1-2} 5 & 25 \\ \cline{1-2} 5 & 5 \\ \cline{1-2} & 1 \end{array}$

$\rule{200}{2}$

Prime factorisation of 200

$\begin{array}{r | l} 2 & 200 \\ \cline{1-2} 2 & 100 \\ \cline{1-2} 2 & 50 \\ \cline{1-2} 5 & 25 \\ \cline{1-2} 5 & 5 \\ \cline{1-2} & 1 \end{array}$

$\rule{200}{2}$

Prime factorisation of 50

$\begin{array}{r | l} 2 & 50 \\ \cline{1-2} 5 & 25 \\ \cline{1-2} 5 & 5 \\ \cline{1-2} & 1 \end{array}$

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