Number Properties Section 7: Roots

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Roots

Finding the square root of a number, or the number that when multiplied by itself equals the original number.

For example:

√2 = 1.414 because 1.414 × 1.414 = 2 (approximately) 

Basic video explaining square roots

Courtesy of Knewton (click for more information)

	"Approximate" Radical Questions? If Jerry has 5 rods that are √2 in length, what is the total length of the rods? a. 4 b, 5 c. 6 d. 7 e. 8 In most standard math tests outside of the GMAT, you would see the answer of 5√2. But, the GMAT sometimes has "approximate" questions where you can "approximate" the value of irrational numbers, such as √2 (as 1.4) or π (as 3.14).

In addition to square roots, there are also cubed roots which mean that when a number is cubed, it will give us the original number (the cubed root of 64 is 4 because 4³ gives us 64).

Higher roots follow the same rule, and if a question asks for a fifth root of a number it means that a number raised to the fifth power will give us the original number. The fifth root of 32 is 2 since 2⁵ = 32.

Roots to Memorize

Root Manipulation Rules

1. You can't add or subtract Radicals
   
   √4 + √9 does not equal √13.
   
   Instead break the radicals into units:
   
   √4 = 2 and √9 = 3 therefore √4 + √9 = 2 + 3 = 5
   
   
2. You can multiply and divide radicals
   (must be the same root - square, cube, etc.)
   
   √4 × √9 = √36 = 6
   
   You can test this
   
   √4 = 2 and √9 = 3 = 2 × 3 = 6
   
   
   √9 ÷ √4 = √2.25 = 1.5
   
   You can test this
   
   (√9 = 3) ÷ (√4 = 2) and 3 ÷ 2 = 1.5
   
   
   
   
   

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Contents of Number Properties Chapter: Table of Contents   Section 1: Number Rules   Section 2: Consecutive Numbers   Section 3: Divisibility   Section 4: Fractions   Section 5: Decimals   Section 6: Exponents   Section 7: Roots & Radicals   Section 8: Sample Questions   Table of Contents

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