How do you simplify $2 \sqrt{20} - \sqrt{20} + 3 \sqrt{20} - 2 \sqrt{45}$ $2sqrt20-sqrt20+3sqrt20-2sqrt45$ ?

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Answer 1 · 2017-11-23T06:25:00

$2 \sqrt{20} - \sqrt{20} + 3 \sqrt{20} - 2 \sqrt{45} = 2 \sqrt{5}$ $2sqrt20-sqrt20+3sqrt20-2sqrt45=2sqrt5$

$2 \sqrt{20} - \sqrt{20} + 3 \sqrt{20} - 2 \sqrt{45}$ $2sqrt20-sqrt20+3sqrt20-2sqrt45$

= $\sqrt{20} (2 - 1 + 3) - 2 \sqrt{3 \times 3 \times 5}$ $sqrt20(2-1+3)-2sqrt(3xx3xx5)$

= $\sqrt{2 \times 2 \times 5} \times 4 - 2 \sqrt{3 \times 3 \times 5}$ $sqrt(color(red)(2xx2)xx5)xx4-2sqrt(color(red)(3xx3)xx5)$

= $2 \times 4 \times \sqrt{5} - 3 \times 2 \times \sqrt{5}$ $color(red)2xx4xxsqrt5-color(red)3xx2xxsqrt5$

= $8 \sqrt{5} - 6 \sqrt{5}$ $8sqrt5-6sqrt5$

= $(8 - 6) \sqrt{5}$ $(8-6)sqrt5$

= $2 \sqrt{5}$ $2sqrt5$

Answer 2 · 2017-11-23T06:49:03

$2 \sqrt{5}$ $2sqrt5$

Simplify
$2 \sqrt{20} - \sqrt{20} + 3 \sqrt{20} - 2 \sqrt{45}$ $2sqrt20 - sqrt20 + 3sqrt20 - 2sqrt45$

1) Combine like terms
Combine all the coefficients of the $\sqrt{20}$ $sqrt20$ terms
$4 \sqrt{20} - 2 \sqrt{45}$ $4sqrt20 - 2sqrt45$

2) Factor to get perfect squares
$4 \sqrt{2^{2} \cdot 5} - 2 \sqrt{3^{2} \cdot 5}$ $4sqrt(2^2*5) - 2sqrt(3^2*5)$

3) Find the square roots, but leave the 5s inside
$(2 \cdot 4) \sqrt{5} - (3 \cdot 2) \sqrt{5}$ $(2*4)sqrt5 - (3*2)sqrt5$

This is the same as
$8 \sqrt{5} - 6 \sqrt{5}$ $8sqrt5 - 6sqrt5$

4) Combine like terms
$2 \sqrt{5} \leftarrow$ $2sqrt5 larr$ answer

Answer:
Simplified, the expression is $2 \sqrt{5}$ $2sqrt5$

How do you simplify 2√20−√20+3√20−2√452sqrt20-sqrt20+3sqrt20-2sqrt45?