
Find the square of 45.
Answer
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Hint: We will first express the given number as a difference of two numbers. We will then apply a suitable algebraic identity to simplify the expression. We will further solve the equation to get the required answer. The square of a number is obtained by multiplying a number by itself.
Formula used:
Complete step-by-step answer:
We are supposed to find the square of 45.
The square of any number can be obtained either by usual multiplication or by the application of appropriate identities.
To find the square of 45, we will apply the identity .
For this, we need to write 45 as a difference of two numbers.
We can write 45 as .
So, .
Here, and .
Let us first find i.e., .
Multiplying the terms, we get
……….
Now, we will find . So,
……….
Finally, let us find i.e., .
Multiplying the terms, we get
……….
Substituting equations , , and in the identity , we get
Adding and subtracting the terms, we get
Hence, the square of 45 is 2025.
Note: We can also solve the above problem by using the identity .
To apply this, we will express 45 as a sum of two numbers.
We can write as .
So, .
Here, and .
Let us first find i.e., .
Multiplying the terms, we get
……….
Now, we will find . So,
……….
Finally, let us find i.e., .
Multiplying the terms, we get
……….
Substituting equations , , and in the identity , we get
Adding the terms, we get
Hence, the square of 45 is 2025.
Formula used:
Complete step-by-step answer:
We are supposed to find the square of 45.
The square of any number can be obtained either by usual multiplication or by the application of appropriate identities.
To find the square of 45, we will apply the identity
For this, we need to write 45 as a difference of two numbers.
We can write 45 as
So,
Here,
Let us first find
Multiplying the terms, we get
Now, we will find
Finally, let us find
Multiplying the terms, we get
Substituting equations
Adding and subtracting the terms, we get
Hence, the square of 45 is 2025.
Note: We can also solve the above problem by using the identity
To apply this, we will express 45 as a sum of two numbers.
We can write
So,
Here,
Let us first find
Multiplying the terms, we get
Now, we will find
Finally, let us find
Multiplying the terms, we get
Substituting equations
Adding the terms, we get
Hence, the square of 45 is 2025.
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