What is the square root of 2 to the poweer of (1/3)?
In order to do the problem, I need this information. We are not allowed to use the calculator so I was wondering what that is, or how to find powers of square roots like this.
sqrt2)^1/3)=1/(sqrt2)^3=1/2sqrt2
= sqrt2/(2sqrt2*sqrt2)=(sqrt2)/4
Ignore that post, I wasn't thinking clearly.
sqrt2^1/3
which is the cube root of sqrt2, or
2^1/6
Now, if you need to find the value of that, without a calculator, you can always use a log table.
To solve the problem, you need to understand both square roots and exponentiation. The square root (√) of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 4 is 2 because 2 * 2 = 4. Exponentiation involves raising a number to a certain power. For instance, 2 raised to the power of 3 (written as 2^3) means multiplying 2 by itself three times: 2 * 2 * 2 = 8.
Now, let's break down the problem step by step. We are asked to find the square root of 2 to the power of (1/3).
1. First, let's find 2 raised to the power of (1/3). The exponent (1/3) represents the cube root (∛). The cube root of a number is a value that, when multiplied by itself three times, gives the original number. In this case, we need to find the cube root of 2.
2. To find the cube root, we need to determine a number that, when raised to the power of 3, gives us 2. Since the cube root of 2 cannot be expressed as a whole number, we will use an approximation.
3. You can approximate the cube root of 2 by using trial and error, or by using a logarithm table. Alternatively, you can use a calculator or an online tool that can calculate cube roots for you.
So, in summary, to solve this problem without using a calculator, you need to understand the concepts of square roots, exponentiation, and how to approximate a cube root.