Question

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

Answer 1

3√45 - √125  + √200 - √50
9 √5 - 5√5  + 10 √2 - 5√2

4 √5 + 5 √2

5 √2 [ 2√2 + 1 ]

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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