Square Root and Cube Root – Properties, Key Differences, Formulas

Square Root and Cube Root - Properties, Key Differences, Formulas

Square Root and Cube Root – Properties, Key Differences, Formulas

In Mathematics, the concept of roots is very important. The concept of square roots and cube roots have been around for a long time. The history of roots takes us back to the Babylonians who first encountered the concept of the square root. They used to compile a list that contained perfect squares and perfect cubes of various numbers. This way they could easily find the square roots and cube roots with problems that include finding the area, volume, and missing length of shapes. They used the concept of square and cube roots in the architecture as well to construct temples, pyramids as well as shrines.

The Egyptians used the word “knbt” for square roots and pronounced it as “kenbet” which means the corner or vertex of a right-angled triangle. The symbol we currently use to represent square roots comes from the Egyptian symbol. After the Egyptians, many other cultures started to use square roots and it emerged as a significant concept in Mathematics.

The concept of square and cube roots can be understood with the help of daily-life objects. This can get students hands-on experience in solving a range of problems related to square and cube roots. Also, each and every topic is interlinked in Mathematics so, understanding the concept of square roots and cube roots students can help students understand other complex concepts. Therefore one needs to focus on the core concepts in order to build a strong mathematical foundation.

In this blog, we will explore square roots and cube roots. We will also study their properties and explore some of the key differences. Let’s dive into the topic:

Square Roots

When we multiply a number by itself, the product is a square number. The number which is multiplied is the square root. Now we can only get perfect square roots for square numbers. We represent square roots by the symbol “√”. If x2 is a square number, then x is a square root of that number.

Properties of Square Roots

● We can get perfect square roots for square numbers only.
● The square root is even for an even perfect square.
● Similarly, the square root is odd, for an odd perfect square.
● A perfect square can never be negative hence the square root of a negative number remains undefined.

Cube Roots

Cube root is an indication of how many times we need to multiply a number in order to get radical. Cube root represents a root of three. So, when the cube root is cubed, it produces the radicant.

Properties of Cube Root

● The cube root is odd for an odd number
● The cube root is even for even numbers.
● The cube root for a negative integer is always negative.

Difference Between Square Root and Cube Root

We now know what a square root and Cube root is. Cuemath is an online learning platform that can help you get an in-depth understanding of square root and cube root with the help of their online classes and different visuals tools. Visual tools can help you visualize the concept of square roots and cube roots.

On the basis of our above discussion on square and cube roots, we can easily differentiate them. While square root is when the two lowest digit numbers are multiplied together two times and in cube root, we multiply the lowest digit number three times. Square roots are basically a reversal of squaring two numbers while cube roots reverse the process of raising the number to the power three. In terms of the symbol of square and cube roots, the symbol of the square root is a radical sign and that of a cube root is a radical sign with a small 3 above to the left side.

 

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