simplify 3√5+√125-5√250+3√400
Answers
Answer:
Answer:
Simplification of
3\sqrt{45}-\sqrt{125}+\sqrt{200}-\sqrt{50}3
45
−
125
+
200
−
50
=4\sqrt{5}+5\sqrt{2}4
5
+5
2
Step-by-step explanation:
Simplification of
3\sqrt{45}-\sqrt{125}+\sqrt{200}-\sqrt{50}3
45
−
125
+
200
−
50
= \begin{gathered}3\sqrt{(3\times3)\times5}-\sqrt{(5\times5)\times5}\\+\sqrt{(10\times10)\times2}-\sqrt{(5\times5)\times2}\end{gathered}
3
(3×3)×5
−
(5×5)×5
+
(10×10)×2
−
(5×5)×2
=3\times3\sqrt{5}-5\sqrt{5}+10\sqrt{2}-5\sqrt{2}3×3
5
−5
5
+10
2
−5
2
= 9\sqrt{5}-5\sqrt{5}+10\sqrt{2}-5\sqrt{2}9
5
−5
5
+10
2
−5
2
=(9-5)\sqrt{5}+(10-5)\sqrt{2}(9−5)
5
+(10−5)
2
= 4\sqrt{5}+5\sqrt{2}4
5
+5
2
Therefore,
Simplification of
3\sqrt{45}-\sqrt{125}+\sqrt{200}-\sqrt{50}3
45
−
125
+
200
−
50
=4\sqrt{5}+5\sqrt{2}4
5
+5
2