The question at hand asks for the value that is equivalent to the square root of the cube root of 5. Let’s break this down into simpler parts for better understanding.
First, we need to find the cube root of 5. The cube root is the number that, when multiplied by itself three times (or raised to the power of 3), gives 5. Mathematically, we can express this as:
\sqrt[3]{5}
So, the cube root of 5 is approximately 1.709975947.
Next, we take the square root of the cube root we just calculated. The square root is the number that, when multiplied by itself two times (or raised to the power of 2), produces the value we derived in the previous step. This is expressed as:
\sqrt{\sqrt[3]{5}}
Now, substituting the cube root value we calculated earlier, we get:
sqrt{1.709975947}
Calculating this gives us approximately 1.307. Hence, the square root of the cube root of 5 is about 1.307.
In conclusion, the value we were looking for, which is equal to the square root of the cube root of 5, is approximately 1.307.