How to simplify a square root
Example: 72 = 36 × 2, and 36 is a perfect square, so √72 = √36 × √2 = 6√2, about 8.4852813742. It lies between √64 = 8 and √81 = 9.
Cube roots work the same way with perfect cubes: 54 = 27 × 2, so ∛54 = 3∛2. Negative numbers have real cube roots (∛−8 = −2) but no real square roots: √−9 is the imaginary number 3i.
Perfect squares to know
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361 and 400 are the squares of 1 to 20. Knowing them makes it quick to estimate any root: √50 is a little over 7, because 49 = 7². Roots of non-perfect squares are irrational, so their decimals never end or repeat; the calculator shows 10 significant digits.
Frequently asked questions
What is the square root of 72 in simplest form?
6√2, because 72 = 36 × 2 and √36 = 6. As a decimal it's about 8.485.
How do you find a cube root?
Find the number that, multiplied by itself three times, gives the original. ∛27 = 3 because 3 × 3 × 3 = 27. For other numbers, raise to the power 1/3.
Can you take the square root of a negative number?
Not among the real numbers. The result is imaginary: √−16 = 4i, where i = √−1.
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