Answer
409.8k+ views
Hint: To write the simplest radical form of a square root we need to factorize a number. Then we will simplify the given expression by finding the square root of 4 and 7. Substituting the values obtained in the given expression gives the simplest radical form.
Complete step by step answer:
We have been given an expression $ \sqrt{\dfrac{4}{49}} $ .
We have to find the simplest radical form.
Now, we know that radical means square root.
We can rewrite the given expression as
$ \Rightarrow \dfrac{\sqrt{4}}{\sqrt{49}} $
Now, we have to solve the obtained expression. We need to calculate the square root of 4 and the square root of 49. We know that when a number is multiplied by itself it is known as the square of that number.
We know that 4 and 49 both are perfect squares so we can factorize both as
$ \begin{align}
& \Rightarrow 4=2\times 2 \\
& \Rightarrow 49=7\times 7 \\
\end{align} $
So we get the values
\[\begin{align}
& \Rightarrow \sqrt{4}=2 \\
& \Rightarrow \sqrt{49}=7 \\
\end{align}\]
Now, substituting the values we get
$ \Rightarrow \dfrac{\sqrt{4}}{\sqrt{49}}=\dfrac{2}{7} $
Now, we get the simplest form as $ \dfrac{2}{7} $ .
Note:
A number of the form $ \sqrt{x} $ is a real number, where $ x $ is called the radicand and the symbol $ \sqrt{{}} $ is known as radical symbol. The word radical in mathematics denotes the root or square root. Every number has two roots either positive or negative.
Complete step by step answer:
We have been given an expression $ \sqrt{\dfrac{4}{49}} $ .
We have to find the simplest radical form.
Now, we know that radical means square root.
We can rewrite the given expression as
$ \Rightarrow \dfrac{\sqrt{4}}{\sqrt{49}} $
Now, we have to solve the obtained expression. We need to calculate the square root of 4 and the square root of 49. We know that when a number is multiplied by itself it is known as the square of that number.
We know that 4 and 49 both are perfect squares so we can factorize both as
$ \begin{align}
& \Rightarrow 4=2\times 2 \\
& \Rightarrow 49=7\times 7 \\
\end{align} $
So we get the values
\[\begin{align}
& \Rightarrow \sqrt{4}=2 \\
& \Rightarrow \sqrt{49}=7 \\
\end{align}\]
Now, substituting the values we get
$ \Rightarrow \dfrac{\sqrt{4}}{\sqrt{49}}=\dfrac{2}{7} $
Now, we get the simplest form as $ \dfrac{2}{7} $ .
Note:
A number of the form $ \sqrt{x} $ is a real number, where $ x $ is called the radicand and the symbol $ \sqrt{{}} $ is known as radical symbol. The word radical in mathematics denotes the root or square root. Every number has two roots either positive or negative.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![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)
How do you graph the function fx 4x class 9 maths 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)