Whenever a number (x) is multiplied 3 times, climate the resultant number is known as the cube of that number. Thus, the cube for the number (x) i do not care x3 or x-cubed. For example, let united state take the number 5. We recognize that 5 × 5 × 5 = 125. Hence, 125 is referred to as the cube of 5. When on the other hand, the cube root of a number is the reverse process of the cube the a number and is denoted through ∛. Considering the very same example, 5 is dubbed the cube source of the number 125. On this page, we will learn an ext about the cubes and also cube root of a number.

You are watching: Simplify square root of 2 multiplied by the cube root of 2

1.What is a Cube Root?
2.How to find Cube source of a Number?
3.What is Cube that a Number?
4.List of Cube root of Numbers
5.FAQs top top Cube Root

What is a Cube Root?

When we think around the indigenous cube and also root, the first picture the might pertained to our psychic is a literal meaning cube and the root of a tree. Isn't it? Well, the idea is similar. Root way the primary resource or origin. So, we just need to think "cube of i m sorry number must be taken to acquire the given number". In mathematics, the an interpretation of cube root is created as, "Cube source is the number that demands to be multiplied three times to obtain the initial number." Now, let united state look at the cube source formula, where y is the cube root of x. ∛x = y. The radical authorize ∛ is supplied as a cube source symbol for any type of number through a little 3 composed on the optimal left of the sign. Another method to denote cube root is to create 1/3 together the exponent that a number.

Cube source is one inverse procedure of the cube that a number.


Perfect Cubes:

A perfect cube is an integer that have the right to be expressed as the product of three exact same or equal integers. Because that example, 125 is a perfect cube due to the fact that 53 = 5 × 5 × 5 = 125. However, 121 is not a perfect cube due to the fact that there is no number, which as soon as multiplied three times offers the product 121. In other words, a perfect cube is a number whose cube root is an integer. The following table mirrors the perfect cubes of the first 10 herbal numbers.

Number/Cube rootPerfect cube

How to uncover Cube source of a Number?

The cube source of a number have the right to be figured out by making use of the prime factorization method. In bespeak to discover the cube source of a number, start with the element factorization of the offered number. Then, division the factors derived into groups containing three very same factors. ~ that, eliminate the cube source symbol and multiply the factors to gain the answer. If over there is any factor left the cannot be separated equally into teams of three, that means the provided number is not a perfect cube and we cannot uncover the cube source of the number. For example, let us see exactly how we discover the cube source of 15625.


What is Cube the a Number?

When we multiply a number 3 times through itself, the result number (product) is well-known as the cube of the original number. We call it a cube because it is used to represent the volume of a cube. In various other words, a number elevated to exponent 3 is dubbed the cube of the number. Because that example, the cube the 3 is 27. That way 3 × 3 × 3 = 27, and also it have the right to be written as 33. Similarly, the cube that 4 is 64, and the cube that 5 is 125, and so on.

To find the cube that a number, first, multiply the number through itself, then multiply the product derived with the initial number again. Let us find the cube the 7 v the very same process. We understand that the cube the a number N is N × N × N. So, the cube of 7 is 7 × 7 × 7. Now, in stimulate to discover the cube the 7, us will an initial find the value of 7 × 7. This worth is 49. Now, us will discover 49 × 7. This is same to 343. Hence, we have the right to say that cube that the number 7 is 343.

Cube the a fraction

Similar come the cube the a number, the cube of a fraction can be uncovered by multiply it 3 times. Because that example, the cube that the portion (2/5) have the right to be composed as 2/5 × 2/5 × 2/5. Simplifying it further, we acquire the value of cube as (2 × 2 × 2) / (5 × 5 × 5). This is same to (23/ 53) = 8/125.

Cube of negative Numbers

The procedure to discover the cube that a negative number is the same as the of a entirety number and also fraction. Here, constantly remember the the cube that a an adverse number is always negative, while the cube that a hopeful number is constantly positive. For example, let us shot finding the cube of -7.

See more: How Fast Is 35 Meters Per Second To Miles Per Hour Converter (M/S To Mph)

We recognize that the cube the -7 is (-7) × (-7) × (-7). Now, in order to discover the cube of (-7), us will first find the worth of (-7) × (-7). This value is 49. Now, us will discover 49 × (-7). This is equal to -343. Hence, we deserve to say that cube of the number -7 is -343.