The simplified value of $\sqrt{72}+\sqrt{800}-\sqrt{18}$ is :
Last updated date: 19th Mar 2023
•
Total views: 304.2k
•
Views today: 2.83k
Answer
304.2k+ views
Hint: The given problem is related to the square root of numbers. Find the square root of the numbers by factorization and then use mathematical operations to evaluate the simplified value of the given expression.
Complete step-by-step answer:
We are asked to find the simplified value of $\sqrt{72}+\sqrt{800}-\sqrt{18}$. First, we will evaluate the value of each term, then find the simplified value of the expression. To find the value of each term, we will determine the value of the square root by factorization.
We know, $72=2\times 2\times 2\times 3\times 3$. So, $\sqrt{72}=\sqrt{2\times 2\times 2\times 3\times 3}$ . We will express the factors as a product of squares of prime numbers. So, $\sqrt{72}=\sqrt{{{2}^{2}}\times {{3}^{2}}\times 2}$.
$=2\times 3\times \sqrt{2}$
$=6\sqrt{2}$
Now, $800=2\times 2\times 2\times 2\times 2\times 5\times 5$ . So, $\sqrt{800}=\sqrt{2\times 2\times 2\times 2\times 2\times 5\times 5}$ . We will express the factors as a product of squares of prime numbers. So, \[\sqrt{800}=\sqrt{{{2}^{2}}\times {{2}^{2}}\times {{5}^{2}}\times 2}\] .
\[=2\times 2\times 5\times \sqrt{2}\]
\[=20\sqrt{2}\]
Now, $18=2\times 3\times 3$ . So, $\sqrt{18}=\sqrt{2\times 3\times 3}$ . We will express the factors as a product of squares of prime numbers. So, $\sqrt{18}=\sqrt{{{3}^{2}}\times 2}$ .
$=3\sqrt{2}$
Now, we have the values of the square root of all the terms given in the expression. Now, we can find the value of the expression. The given expression is $\sqrt{72}+\sqrt{800}-\sqrt{18}$ . We have calculated the values of $\sqrt{72},\sqrt{800}$ and $\sqrt{18}$ as $20\sqrt{2}$ , $3\sqrt{2}$ , and $6\sqrt{2}$ respectively. Now, we will substitute the values of $\sqrt{72},\sqrt{800}$ and $\sqrt{18}$ in the given expression. On substituting the values of $\sqrt{72},\sqrt{800}$ and $\sqrt{18}$ in the given expression, we get:
$\sqrt{72}+\sqrt{800}-\sqrt{18}=6\sqrt{2}+20\sqrt{2}-3\sqrt{2}$
Now, we will take $\sqrt{2}$ common from all three terms. On taking $\sqrt{2}$ common from all three terms, we get $\sqrt{72}+\sqrt{800}-\sqrt{18}=\left( 6+20-3 \right)\sqrt{2}=23\sqrt{2}$.
Hence, the simplified value of the expression $\sqrt{72}+\sqrt{800}-\sqrt{18}$ is equal to $23\sqrt{2}$ .
Note: While evaluating the square root of a number, it is better to express the number as a product of its prime factors. This way, it will be easier to calculate the square root and there will be no confusion while evaluating the square root.
Complete step-by-step answer:
We are asked to find the simplified value of $\sqrt{72}+\sqrt{800}-\sqrt{18}$. First, we will evaluate the value of each term, then find the simplified value of the expression. To find the value of each term, we will determine the value of the square root by factorization.
We know, $72=2\times 2\times 2\times 3\times 3$. So, $\sqrt{72}=\sqrt{2\times 2\times 2\times 3\times 3}$ . We will express the factors as a product of squares of prime numbers. So, $\sqrt{72}=\sqrt{{{2}^{2}}\times {{3}^{2}}\times 2}$.
$=2\times 3\times \sqrt{2}$
$=6\sqrt{2}$
Now, $800=2\times 2\times 2\times 2\times 2\times 5\times 5$ . So, $\sqrt{800}=\sqrt{2\times 2\times 2\times 2\times 2\times 5\times 5}$ . We will express the factors as a product of squares of prime numbers. So, \[\sqrt{800}=\sqrt{{{2}^{2}}\times {{2}^{2}}\times {{5}^{2}}\times 2}\] .
\[=2\times 2\times 5\times \sqrt{2}\]
\[=20\sqrt{2}\]
Now, $18=2\times 3\times 3$ . So, $\sqrt{18}=\sqrt{2\times 3\times 3}$ . We will express the factors as a product of squares of prime numbers. So, $\sqrt{18}=\sqrt{{{3}^{2}}\times 2}$ .
$=3\sqrt{2}$
Now, we have the values of the square root of all the terms given in the expression. Now, we can find the value of the expression. The given expression is $\sqrt{72}+\sqrt{800}-\sqrt{18}$ . We have calculated the values of $\sqrt{72},\sqrt{800}$ and $\sqrt{18}$ as $20\sqrt{2}$ , $3\sqrt{2}$ , and $6\sqrt{2}$ respectively. Now, we will substitute the values of $\sqrt{72},\sqrt{800}$ and $\sqrt{18}$ in the given expression. On substituting the values of $\sqrt{72},\sqrt{800}$ and $\sqrt{18}$ in the given expression, we get:
$\sqrt{72}+\sqrt{800}-\sqrt{18}=6\sqrt{2}+20\sqrt{2}-3\sqrt{2}$
Now, we will take $\sqrt{2}$ common from all three terms. On taking $\sqrt{2}$ common from all three terms, we get $\sqrt{72}+\sqrt{800}-\sqrt{18}=\left( 6+20-3 \right)\sqrt{2}=23\sqrt{2}$.
Hence, the simplified value of the expression $\sqrt{72}+\sqrt{800}-\sqrt{18}$ is equal to $23\sqrt{2}$ .
Note: While evaluating the square root of a number, it is better to express the number as a product of its prime factors. This way, it will be easier to calculate the square root and there will be no confusion while evaluating the square root.
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
