Question

Find the value of ³√8 + ³√27 +³ √64

Answer 1

$\displaystyle \sf{ \sqrt[3]{8} + \sqrt[3]{27} + \sqrt[3]{64} } = 9$

Correct question : Find the value of $\displaystyle \sf{ \sqrt[3]{8} + \sqrt[3]{27} + \sqrt[3]{64} }$

Given :

The expression $\displaystyle \sf{ \sqrt[3]{8} + \sqrt[3]{27} + \sqrt[3]{64} }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ \sqrt[3]{8} + \sqrt[3]{27} + \sqrt[3]{64} }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ \sqrt[3]{8} + \sqrt[3]{27} + \sqrt[3]{64} }$

$\displaystyle \sf{ = \sqrt[3]{ {2}^{3} } + \sqrt[3]{ {3}^{3} } + \sqrt[3]{ {4}^{3} } }$

$\displaystyle \sf{ = 2 + 3 + 4}$

$\displaystyle \sf{ = 9}$

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Answer 2

³√8 + ³√27 + ³√64 = 2 + 3 + 4 = 9.

We can simplify each of the cube roots and then add them up.

³√8 = 2, because 2 x 2 x 2 = 8.

³√27 = 3, because 3 x 3 x 3 = 27.

³√64 = 4, because 4 x 4 x 4 = 64.

So,

³√8 + ³√27 + ³√64 = 2 + 3 + 4 = 9.

Therefore, the value of the expression is 9.

In mathematics, a cube root of a number x is a number y such that y³ = x. All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots.
For example, the cube root of 8 is 2 because 2³ (2 multiplied by itself three times) equals 8. Similarly, the cube root of -27 is -3 because -3³ equals -27.

The cube root can be calculated using various methods such as long division, prime factorization, or estimation. In modern times, it can also be easily calculated using a calculator or computer software.

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