
How do you simplify ?
Answer
468k+ views
Hint: We will first find the prime factorisation of both 5 and 15. Then we will make use of the fact that . Then, we will take out the factors which are common in both the numbers and thus we have the answer.
Complete step by step solution:
We are given that we are required to simplify .
We have two numbers involved here, 5 and 15.
We know that 5 is itself a prime number, therefore, it cannot be broken into further factors.
And, we also know that 15 is divisible by both 5 and 3. Therefore, 15 can be written as multiple of 3 and 5.
Therefore, we can write it as follows:-
Now, we know that we have the following expression as a fact:-
For any non – negative real numbers a and b, we have: .
Replacing a by 5 and b by 15, we will get the following expression with us:-
Since we know that 15 is divisible by both 5 and 3. Therefore, 15 can be written as multiple of 3 and 5.
Therefore, we can write the above mentioned expression as follows:-
We observe that 5 is twice inside the square root given above on the right hand side, therefore, we can take 1 5 out of the square root and get the following expression:-
Thus, we have the required answer.
Note: The students must commit to the memory the following formula:-
For any non – negative real numbers a and b, we have: .
We can also prove it as follows:-
If we have two negative real numbers a and b, then we can write as .
Complete step by step solution:
We are given that we are required to simplify
We have two numbers involved here, 5 and 15.
We know that 5 is itself a prime number, therefore, it cannot be broken into further factors.
And, we also know that 15 is divisible by both 5 and 3. Therefore, 15 can be written as multiple of 3 and 5.
Therefore, we can write it as follows:-
Now, we know that we have the following expression as a fact:-
For any non – negative real numbers a and b, we have:
Replacing a by 5 and b by 15, we will get the following expression with us:-
Since we know that 15 is divisible by both 5 and 3. Therefore, 15 can be written as multiple of 3 and 5.
Therefore, we can write the above mentioned expression as follows:-
We observe that 5 is twice inside the square root given above on the right hand side, therefore, we can take 1 5 out of the square root and get the following expression:-
Thus, we have the required answer.
Note: The students must commit to the memory the following formula:-
For any non – negative real numbers a and b, we have:
We can also prove it as follows:-
If we have two negative real numbers a and b, then we can write
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