Question

simplify 3 root 45-root 125+root 200- root 50

Answer 1

3√45= 3√9×5= 3×3√5=9√5
√125=√25×5=5√5
√200= √100×2= 10√2
√50= √25×2= 5√2
Here,
9√5-5√5+10√2-5√2
= 4√5+5√2

Answer 2

Answer:

Simplification of

$3\sqrt{45}-\sqrt{125}+\sqrt{200}-\sqrt{50}$

=$4\sqrt{5}+5\sqrt{2}$

Step-by-step explanation:

Simplification of

$3\sqrt{45}-\sqrt{125}+\sqrt{200}-\sqrt{50}$

= $3\sqrt{(3\times3)\times5}-\sqrt{(5\times5)\times5}\\+\sqrt{(10\times10)\times2}-\sqrt{(5\times5)\times2}$

=$3\times3\sqrt{5}-5\sqrt{5}+10\sqrt{2}-5\sqrt{2}$

= $9\sqrt{5}-5\sqrt{5}+10\sqrt{2}-5\sqrt{2}$

=$(9-5)\sqrt{5}+(10-5)\sqrt{2}$

= $4\sqrt{5}+5\sqrt{2}$

Therefore,

Simplification of

$3\sqrt{45}-\sqrt{125}+\sqrt{200}-\sqrt{50}$

=$4\sqrt{5}+5\sqrt{2}$

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