What is the Relationship between Perfect Squares and Square Roots?
Square Root and Perfect Square
Square root and perfect square. The square root of a number is the reverse of squaring a number, or raising a number to the second power. The square root is the number that when multiplied by itself equals that value. For instance, the square root of 4 is 2 because 2 times itself is 4.
4 is a perfect square. A perfect square is a value that has a whole number square root. The square root of 4 is 2, so it’s square root is a whole number, which means the four is a perfect square. Another example of a perfect square is 9.
The square root of 9 is 3. The square root is a whole number which means that 9 is a perfect square. The square root is 3. 3 is not a perfect square because the square root of 3 is not a whole number. The square root 3 is actually an irrational number.
You can find the value on your calculator, but it does go on forever and ever. Roots can be expressed in exponential form as fractions. The square root of 3 we could write is 3 to the 1/2 power. These are equivalent.
You could write, the cube root of 8 also as a fraction, as an exponent with a fraction, so that be 8 to 1/3 power. The cube root of eight, It’s very similar to finding the square root of a number, but when you find the cube root you’re finding what number times itself three times gives you eight.
The cube of eight is 2 because 2 times 2 times 2 is 8. Some roots have coefficients, like 4 square roots of 7. The coefficient is the number in front of the radical, and if there isn’t a coefficient shown, like with these numbers the square root of 4, square root of 9, square root of 3, or the cube root of 8, then it’s understood to be 1 since one times any number is itself.
But, this coefficient is just a number that’s multiplied by the radical like 4 times the square root of 7, and it’s written without any multiplication sign which is understood that this is 4 times the square root of seven.