Question

Send simply this question step by step

Answer 1

Question:

Simplify:-

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

Answer:

$\sqrt{5}$

Solution:

Let us simplify them term-wise,

We know the factors of:

45 = 1, 3, 9, 15 and 45

20 = 1, 2, 4, 5 and 20

The numbers which are making perfect squares are 9 (3×3) and 4 (2×2).

$\sqrt{45} = \sqrt{3 \times 3 \times 5} \\ \\ 3\sqrt{20} = 3\sqrt{2 \times 2 \times 5}$

Now,

$\implies\sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5} \\ \\\implies\sqrt{3 \times 3 \times 5} - 3 \sqrt{2 \times 2 \times 5} + 4 \sqrt{5} \\ \\\implies 3 \sqrt{5} - 6 \sqrt{5} + 4 \sqrt{5} \\ \\ \implies \sqrt{5} (3 - 6 + 4) \\ \\ \implies \sqrt{5} (1) = \sqrt{5}$

Answer 2

Step-by-step explanation:

GIVEN:

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

WORKING:

SIMPLIFY IT.

SOLUTION:

$\sqrt{45} = 3 \sqrt{5} \\ \\ 3 \sqrt{20} = 6 \sqrt{5}$

NOW SIIMPLIFYING IT;

$\sqrt{45} - 3 \sqrt{20} + 4 \sqrt{5} \\ \\ = 3 \sqrt{5} - 6 \sqrt{5} + 4 \sqrt{5} \\ \\ = 7 \sqrt{5} - 6 \sqrt{5} = \sqrt{5}$