# Find the square root of 1024. Hence find the value of $\sqrt {10.24} + \sqrt {0.1024} + \sqrt {10240000} $.

Last updated date: 27th Mar 2023

•

Total views: 218.2k

•

Views today: 3.94k

Answer

Verified

218.2k+ views

Hint: Here, we will be representing the number (whose square root is to be calculated) as the product of prime factors.

As we know that $1024 = {2^{10}}$

Taking square root on both sides on the above equation, we get

\[ \Rightarrow \sqrt {1024} = \sqrt {{{\left( 2 \right)}^{10}}} = {\left( 2 \right)^{\dfrac{{10}}{2}}} = {2^5} = 32\]

So, the square root of 1024 is 32.

Also, $\sqrt {10.24} + \sqrt {0.1024} + \sqrt {10240000} = \sqrt {\dfrac{{1024}}{{100}}} + \sqrt {\dfrac{{1024}}{{10000}}} + \sqrt {10240000} = \dfrac{{\sqrt {1024} }}{{\sqrt {100} }} + \dfrac{{\sqrt {1024} }}{{\sqrt {10000} }} + \left( {\sqrt {1024} } \right)\left( {\sqrt {10000} } \right)$

Since we already calculated \[\sqrt {1024} = 32\] and now using this, we get

$\sqrt {10.24} + \sqrt {0.1024} + \sqrt {10240000} = \dfrac{{32}}{{10}} + \dfrac{{32}}{{100}} + \left( {32} \right)\left( {100} \right) = 3.2 + 0.32 + 3200 = 3203.52$

Therefore the value of $\sqrt {10.24} + \sqrt {0.1024} + \sqrt {10240000} $ is 3203.52.

Note: The square root of division of two functions is equal to the division of square roots of these two functions i.e.,$\sqrt {\dfrac{{f\left( x \right)}}{{g\left( x \right)}}} = \dfrac{{\sqrt {f\left( x \right)} }}{{\sqrt {g\left( x \right)} }}$ and the square root of product of two functions is equal to the product of square root of these two functions i.e., $\sqrt {f\left( x \right)g\left( x \right)} = \left( {\sqrt {f\left( x \right)} } \right)\left( {\sqrt {g\left( x \right)} } \right)$.

The most common way to make mistakes in such problems is to inappropriately represent the decimal point.

As we know that $1024 = {2^{10}}$

Taking square root on both sides on the above equation, we get

\[ \Rightarrow \sqrt {1024} = \sqrt {{{\left( 2 \right)}^{10}}} = {\left( 2 \right)^{\dfrac{{10}}{2}}} = {2^5} = 32\]

So, the square root of 1024 is 32.

Also, $\sqrt {10.24} + \sqrt {0.1024} + \sqrt {10240000} = \sqrt {\dfrac{{1024}}{{100}}} + \sqrt {\dfrac{{1024}}{{10000}}} + \sqrt {10240000} = \dfrac{{\sqrt {1024} }}{{\sqrt {100} }} + \dfrac{{\sqrt {1024} }}{{\sqrt {10000} }} + \left( {\sqrt {1024} } \right)\left( {\sqrt {10000} } \right)$

Since we already calculated \[\sqrt {1024} = 32\] and now using this, we get

$\sqrt {10.24} + \sqrt {0.1024} + \sqrt {10240000} = \dfrac{{32}}{{10}} + \dfrac{{32}}{{100}} + \left( {32} \right)\left( {100} \right) = 3.2 + 0.32 + 3200 = 3203.52$

Therefore the value of $\sqrt {10.24} + \sqrt {0.1024} + \sqrt {10240000} $ is 3203.52.

Note: The square root of division of two functions is equal to the division of square roots of these two functions i.e.,$\sqrt {\dfrac{{f\left( x \right)}}{{g\left( x \right)}}} = \dfrac{{\sqrt {f\left( x \right)} }}{{\sqrt {g\left( x \right)} }}$ and the square root of product of two functions is equal to the product of square root of these two functions i.e., $\sqrt {f\left( x \right)g\left( x \right)} = \left( {\sqrt {f\left( x \right)} } \right)\left( {\sqrt {g\left( x \right)} } \right)$.

The most common way to make mistakes in such problems is to inappropriately represent the decimal point.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

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

Tropic of Cancer passes through how many states? Name them.

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

Name the Largest and the Smallest Cell in the Human Body ?