3√(32)–³
please solution
Answers
Answer:
2
3
4
+7
3
32
−
3
500
=11
3
4
Step-by-step explanation:
Given : Expression 2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500}2
3
4
+7
3
32
−
3
500
To find : Simplify the expression ?
Solution :
Expression 2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500}2
3
4
+7
3
32
−
3
500
where values can be written as,
32=2\times 2\times 2\times 2\times 232=2×2×2×2×2
i.e. \sqrt[3]{32}=2\times \sqrt[3]{4}
3
32
=2×
3
4
500=4\times 5\times 5\times 5500=4×5×5×5
i.e. \sqrt[3]{500}=5\times \sqrt[3]{4}
3
500
=5×
3
4
Substitute in the equation,
=2\sqrt[3]{4}+7(2\sqrt[3]{4})-5\sqrt[3]{4}=2
3
4
+7(2
3
4
)−5
3
4
=2\sqrt[3]{4}+14\sqrt[3]{4}-5\sqrt[3]{4}=2
3
4
+14
3
4
−5
3
4
=\sqrt[3]{4}(2+14-5)=
3
4
(2+14−5)
=11\sqrt[3]{4}=11
3
4
Therefore, 2\sqrt[3]{4}+7\sqrt[3]{32}-\sqrt[3]{500}=11\sqrt[3]{4}2
3
4
+7
3
32
−
3
500
=11
3
4
#Learn more
Simplify: √(3+2√2)
Step-by-step explanation:
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