Answer
384.9k+ views
Hint:We try to form the indices formula for the value 2. This is a multiplication of square root of 5 and square root of 125. We find the prime factorisation of 125. Then we take one digit out of the two same number of primes from the multiplication. There will be no odd number of primes remaining in the root which can’t be taken out. We keep the square root in its simplest form.
Complete step by step solution:
We need to find the value of the multiplication of the square root of 5 times the square root of 125.
This is a square root form.
The given value is the form of indices. We are trying to find the root value of 125.
We know the theorem of indices \[{{a}^{\dfrac{1}{n}}}=\sqrt[n]{a}\]. Putting value 2 we get
\[{{a}^{\dfrac{1}{2}}}=\sqrt[2]{a}=\sqrt{a}\].
We need to find the prime factorisation of the given number 125.
$\begin{align}
& 5\left| \!{\underline {\,
125 \,}} \right. \\
& 5\left| \!{\underline {\,
25 \,}} \right. \\
& 5\left| \!{\underline {\,
5 \,}} \right. \\
& 1\left| \!{\underline {\,
1 \,}} \right. \\
\end{align}$
Therefore, \[125=5\times 5\times 5\].
For finding the square root, we need to take one digit out of the two same number of primes.
The multiplied terms are \[\sqrt{5}\] and \[\sqrt{125}\].
So, the multiplication is \[\sqrt{5}\times \sqrt{125}=\sqrt{5\times 5\times 5\times 5}\].
This means in the square root value we will take out two fives from the multiplication.
So, \[\sqrt{5}\times \sqrt{125}=\sqrt{5\times 5\times 5\times 5}=5\times 5=25\].
Note: We can also use the variable form where we can take $x=\sqrt[2]{625}$. But we need to remember that we can’t use the cube on both sides of the equation $x=\sqrt[2]{625}$ as in that case we are taking two extra values as a root value. Then this linear equation becomes a cubic equation.
Complete step by step solution:
We need to find the value of the multiplication of the square root of 5 times the square root of 125.
This is a square root form.
The given value is the form of indices. We are trying to find the root value of 125.
We know the theorem of indices \[{{a}^{\dfrac{1}{n}}}=\sqrt[n]{a}\]. Putting value 2 we get
\[{{a}^{\dfrac{1}{2}}}=\sqrt[2]{a}=\sqrt{a}\].
We need to find the prime factorisation of the given number 125.
$\begin{align}
& 5\left| \!{\underline {\,
125 \,}} \right. \\
& 5\left| \!{\underline {\,
25 \,}} \right. \\
& 5\left| \!{\underline {\,
5 \,}} \right. \\
& 1\left| \!{\underline {\,
1 \,}} \right. \\
\end{align}$
Therefore, \[125=5\times 5\times 5\].
For finding the square root, we need to take one digit out of the two same number of primes.
The multiplied terms are \[\sqrt{5}\] and \[\sqrt{125}\].
So, the multiplication is \[\sqrt{5}\times \sqrt{125}=\sqrt{5\times 5\times 5\times 5}\].
This means in the square root value we will take out two fives from the multiplication.
So, \[\sqrt{5}\times \sqrt{125}=\sqrt{5\times 5\times 5\times 5}=5\times 5=25\].
Note: We can also use the variable form where we can take $x=\sqrt[2]{625}$. But we need to remember that we can’t use the cube on both sides of the equation $x=\sqrt[2]{625}$ as in that case we are taking two extra values as a root value. Then this linear equation becomes a cubic equation.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)