Question

$\sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5}$
simplify.​

Answer 1

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Refer attachment.

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Answer 2

Answer:

√5

Step-by-step explanation:

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

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Prime Factorisation of 45 :

→ 3 × 3 × 5

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Prime Factorisation of 20 :

→ 2 × 2 × 5

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On further solving the problem, we get

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

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

Rearranging the terms, we get

→ ${\sf{ 3 {\sqrt{5}} + 4 {\sqrt{5}} - 6 {\sqrt{5}} }}$

→ ${\sf{ 7 {\sqrt{5}} - 6 {\sqrt{5}} }}$

→ ${\boxed{\sf{ {\sqrt{5}} }}}$