Question

ex 3 square root of 10 = 2.15 can any one help me how this came to be the answer?

Answer 1

That's the cube root, not the 3 square root. If \(x = \sqrt[3]{10}\), \(x*x*x =x^3 = 10\). Is your question how do you find the numeric value?

Answer 2

yes, well the book says the answer is 2.15, so im trying to figure out how did they came up with that answer.

Answer 3

Lots of different ways. The easiest is with a calculator that has a cube root key, or with logarithms, or even repeated estimation, depending on how many digits of accuracy you need. For example, we know that it is somewhere between 2 and 3, because 2*2*2=8 and 3*3*3 =27. From that you might guess it is closer to 2, say 2.25, and 2.25*2.25*2.25 = 11.39, so maybe we try halfway between 2 and 2.25, which is 2.125. 2.125*2.125*2.125 = 9.596. Continue that process until it is sufficiently close for your needs.

Another would be with logarithms. \[\sqrt[3]{x} = x^{1/3}\]We could take the log of \(x\), divide it by 3, and take the antilog to get our answer. Any decent calculator will have log functions.

If the calculator has a \(y^x\) button or something similar, you can take an nth root (\(\sqrt[n]{x}\)) by raising \(x^{1/n}\).