Question

simplify:
$\sqrt{45 - 3 \sqrt{20 + 4 \sqrt{5} } }$
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Answer 1

ANSWER

Question:

• $\sqrt{45} - 3\sqrt{20} + 4\sqrt{5}$

(The question mentioned by the user, couldn’t be simplified without putting the values of surds)

Answer:

$:\longrightarrow \sqrt{45} - 3\sqrt{20} + 4\sqrt{5} \\\\\text{We cannot add or subtract unlike surds, so we convert into like surds.} \\\\:\implies \sqrt{(9*5)} - 3\sqrt{(4*5)} + 4\sqrt{5} \\\\:\implies 3\sqrt{5} - (3*2)\sqrt{5} +4\sqrt{5} \\\\:\implies 3\sqrt{5} - 6\sqrt{5} +4\sqrt{5} \\\\:\implies 7\sqrt{5} - 6\sqrt{5} \\\\\bf{:\implies \sqrt{5}}$

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\sf{ \sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5} }$

$\sf{ = \sqrt{9 \times 5} - 3 \sqrt{4 \times 5} + 4 \sqrt{5} }$

$\sf{ = 3 \sqrt{5} - 3 \times 2 \sqrt{5} + 4 \sqrt{5} }$

$\sf{ = (3 - 6 + 4) \sqrt{5} }$

$\sf{ = \sqrt{5} } \: \: \: \: \bf{Ans.}$