Find the square root of 1024. Hence find the value of $\sqrt {10.24} + \sqrt {0.1024} + \sqrt {10240000} $.
Answer
292.6k+ 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
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
What is 1 divided by 0 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the past tense of read class 10 english CBSE

What is pollution? How many types of pollution? Define it

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

How many crores make 10 million class 7 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
