brightchamps-logo
hamburger

open_icon Table Of Contents

LIGHT_BULB_MATHS_BLOG
scholar-purple-hat122 Learners

Last updated on November 30th, 2024

maths_whiteboard

Cube Root of 10

maths_mascot
Foundation
Intermediate
Advance Topics

The cube root of 10 is the value that, when multiplied by itself three times (cubed), gives the original number 10. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.

GREEN_BACKGROUND_HEADING_MASCOT

What Is the Cube Root of 10?

The cube root of 10 is 2.15443469003. The cube root of 10 is expressed as βˆ›10 in radical form, where the “ βˆ› “  sign is called the “radical” sign. In exponential form, it is written as (10)1/3. If “m” is the cube root of 10, then, m3=10. Let us find the value of “m”.
 

GREEN_BACKGROUND_HEADING_MASCOT

Finding the Cube Root of 10

The cube root of 10 is expressed as βˆ›10 as its simplest radical form. We can find cube root of 10 through a method, named as, Halley’s Method. Let us see how it finds the result.

GREEN_BACKGROUND_HEADING_MASCOT

Cube Root of 10 By Halley’s Method

Now, what is Halley’s Method?

It is an iterative method for finding cube roots of a given number N, such that, x3=N, where this method approximates the value of “x”.


Formula is βˆ›a≅ x((x3+2a) / (2x3+a)), where


a=given number whose cube root you are going to find


x=integer guess for the cubic root


 Let us apply Halley’s method on the given number 10.


Step 1: Let a=10. Let us take x as 2, since, 23=8 is the nearest perfect cube which is less than 10.


Step 2: Apply the formula.  βˆ›10≅ 2((23+2×10) / (2(2)3+10))=2.15


Hence, 2.15 is the approximate cubic root of 10.
 

GREEN_BACKGROUND_HEADING_MASCOT

Important Glossaries for Cube Root of 10

  • Irrational Numbers - Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers.

 

  • Whole numbers - The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. 

 

  • Square root - The square root of a number is a value “y” such that when “y” is multiplied by itself → y × y, the result is the original number.

 

  • Polynomial - It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.

 

  • Approximation - Finding out a value which is nearly correct, but not perfectly correct.