Select Page

Square roots and Cube roots

Home >> Online Math Tutoring >> 8th Grade Math Tutoring >> Square roots and Cube roots

Square Roots

The square root of a positive number ‘n’ is that number which, when multiplied by itself, gives ‘n’.

There are two square roots for a positive number. For example, the square roots of 25 are +5 and -5. The positive square root of a number is called the principal square root.

The symbol √ is called the radical sign. The index notation is also used instead of the radical sign. For example:

\sqrt{16} = +4 can be written as 16^{1/2} = +4 .

Example: Find the square root of 81.

81 = 9 × 9

\sqrt{81}= 9

Cube Roots

The cube root of a positive number ‘N’ is that number which, when multiplied by itself twice, gives ‘N’.

For example, the cube root of 8 is 2 because 2 × 2 × 2 = 8 (here 2 is being multiplied by itself twice)

The symbol for cube root is a radical sign with a small 3 on the left ∛ .

Example: Find the cube root of -125.

-125 = (-5)3 = -5 × -5 × -5

\sqrt[3]{-125} = -5

Example: Simplify: \sqrt[3]{343} – \sqrt{196} + 4

7 × 7 × 7 = 343, so  \sqrt[3]{343} = 7

14 × 14 = 196, so \sqrt{196} = 14

so , \sqrt[3]{343} – \sqrt{196} + 4 = 7 – 14 + 4 = 11 -14 = -3

evaluation1

 

  1. Find the square root of 169.
  2. What is the cube root of 1331?
  3. Simplify: \sqrt{225} + \sqrt[3]{-729} – 5
  4. Value of \sqrt[3]{216} – \sqrt[3]{-216}
  5. What is the square root of 1,024?
Answer key
  1. 13
  2. 11
  3. 1
  4. 12
  5. 32

Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. Come to eTutorWorld for Expert Tutors and best K-12 Online Tutoring Services in the comfort and safety of your home at an affordable cost. Find a tutor online for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. Get free printable math and science worksheets in pdf format and SCAT Practice Tests. Sign up for a Free Trial Lesson Today!

© 2018 eTutorWorld - Online Tutoring and Test Prep | All rights reserved