Consider the number 9. When 3 multiplied by itself, it gives 9 as the product. When the exponent is 2, it is called a square. In other words, it is the number that we multiply by itself to get the original number. It is very easy to find the square root of a number that is a perfect square. Perfect squares are those positive numbers that can be written as the multiplication of a number by itself.
We can use four methods to find the square root of numbers and those methods are as follows:. Please note that the first three methods can be conveniently used for perfect squares , while the fourth method, i. This is a very simple method. We will subtract the consecutive odd numbers from the number for which we are finding the square root, till we reach 0.
The number of times we subtract is the square root of the given number. This method works only for perfect square numbers. Let us find the square root of 16 using this method.
Prime factorization of any number means to represent that number as a product of prime numbers. To find the square root of a given number through the prime factorization method, we follow the steps given below:.
Estimation and approximation refer to a reasonable guess of the actual value to make calculations easier and realistic. This method helps in estimating and approximating the square root of a given number. Find the nearest perfect square numbers to Let us consider 3. Let us find the squares of 3. We can repeat the process and check between 3.
Long Division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps.
We can find the exact square root of any given number using this method. Let us understand the process of finding square root by the long division method with an example. Let's find the square root of Step 3: Bring down the number under the next bar to the right of the remainder.
How do you find a square root without a calculator? What is the fourth square root of ? What are the real fourth roots of 81? What is a perfect 4th power? Why is 4 square root 16? Long Division Method. What is the relationship between squares and square roots? Ans: Both square roots and squares are concepts that are opposite in nature.
Squares are the numbers that are produced when a value is multiplied by itself. The square root of a number, on the other hand, is a value that, when multiplied by itself, returns the original value.
What are perfect squares and square roots? Ans: The square root is the number that equals that value when multiplied by itself. A value with a whole number square root is called a perfect square. Why is it important to learn the squares and square roots of the numbers?
Ans: A square root is a number that equals that value when multiplied by itself. A value with a whole number square root is referred to as a perfect square. What are the roots of perfect squares? A perfect square is when we are simplifying a square root and nothing remains under the radical. What are the square roots of 36, 81, and ? Pause the video and try these on your own. We get these nice, pretty numbers because we are taking the square roots of perfect squares.
Well, then we will have to simplify the square root. When simplifying a square root, we will get all the perfect squares out from under the radical and whatever is remaining from the factors of the radicand stays under the radical. There are no more perfect squares to take out, so we simply multiply these numbers together to get our new radicand.
Now I want you to try one. Simplify the square root of Pause the video here and simplify.
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