evaluate ³√27+³√0.008+³√0.064
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Step-by-step explanation:
Given : Expression \sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}
3
27
+
3
0.008
+
3
0.064
To find : Evaluate the expression ?
Solution :
\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}
3
27
+
3
0.008
+
3
0.064
=\sqrt[3]{3\times 3\times 3}+\sqrt[3]{0.2\times 0.2\times 0.2}+\sqrt[3]{0.4\times 0.4\times 0.4}=
3
3×3×3
+
3
0.2×0.2×0.2
+
3
0.4×0.4×0.4
=\sqrt[3]{3^3}+\sqrt[3]{0.2^2}+\sqrt[3]{0.4^2}=
3
3
3
+
3
0.2
2
+
3
0.4
2
We know, \sqrt[a]{x^a}=x
a
x
a
=x
=3+0.2+0.4=3+0.2+0.4
=3.6=3.6
Therefore, \sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}=3.6
3
27
+
3
0.008
+
3
0.064
=3.6
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