Question

find the cube roots of the following: -9261*512​

Answer 1

Answer:

sorry I have square root

Answer 2

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To Find:

• Cube root of -9261*512

Solution:

We will first calculate the cube root of -9261 and then multiply it with cube root of 512.

$\implies \sqrt[3]{-9261*512} \\\implies \sqrt[3]{-9261}*\sqrt[3]{512} ---(A)$

$\\ \text{Prime factors of -9261 \longrightarrow }\\\\ \Large{ \begin{array}{c|c} \tt 3 & \sf{-9261} \\ \cline{1-2} \tt 3 & \sf {-3087} \\ \cline{1-2} \tt 3 & \sf{-1029} \\ \cline{1-2} \tt 7 & \sf{-343}\\ \cline{1-2} \tt 7 & \sf{-49}\\ \cline{1-2} \tt 7 & \sf{-7}\\ \cline{1-2} \tt -1 & \sf{-1} \\ \cline{1-2} & \sf{1} \end{array}} \\ \\ \implies -9261 = 3*3*3*7*7*7*(-1) \\\implies -9261 = (-3)^3 * 7^3 \:\:\:\:\:\:OR\:\:\:\:\:\: -9261 = 5^3 * (-7)^3 \\\implies -9261 = -21^3------(1)$

$\\ \text{Prime factors of 512 \longrightarrow }\\\\ \Large{ \begin{array}{c|c} \tt 2 & \sf{512} \\ \cline{1-2} \tt 2 & \sf {256} \\ \cline{1-2} \tt 2 & \sf{128} \\ \cline{1-2} \tt 2 & \sf{64}\\ \cline{1-2} \tt 2 & \sf{32}\\ \cline{1-2} \tt 2 & \sf{16}\\ \cline{1-2} \tt 2 & \sf{8} \\ \cline{1-2} \tt 2 & \sf{4}\\ \cline{1-2} \tt 2 & \sf{2} \\ \cline{1-2} & \sf{1} \end{array}} \\ \\ \implies 512 = 2*2*2*2*2*2*2*2*2 \\\implies 512 = 2^9 \\\implies 512 = (2^3)^3\\\implies 512= 8^3------(2)$

Put, (1) & (2) in (A)...

$\implies \sqrt[3]{-9261}*\sqrt[3]{512} \\\implies \sqrt[3]{(-21)^3}*\sqrt[3]{(8)^3} \\\implies (-21)^{\frac{3}{3}} * (8)^{\frac{3}{3}} \\\implies -21 * 8 \\\bf{\implies -168}$

Cube root of -9261*512 is 168.

HOPE IT HELPS!!!