Question

The square root of 1$\frac{13}{36}$ is?

Answer 1

Answer:

7/6

Step-by-step explanation:

As per the provided information in the given question, we have been asked to calculate the,

• $\sf \sqrt{1\dfrac{13}{36}}$

Basically firstly we need to convert the mixed fraction into proper fraction after that we'll solve further using the indices identities.

Indices identities to remember while solving this type of questions :

$\small \boxed{ \begin{array}{cc} { \sf{ \star \: \: {( \sqrt{a} )}^{2} = a } } \\ \\ \star \: \: \sf \sqrt{a} \sqrt{b} = \sqrt{ab} \\ \\ \star \: \: \sf \dfrac{ \sqrt{a} }{ \sqrt{b} } = \sqrt{ \dfrac{a}{b} } \\ \\ \star \: \: \sf( \sqrt{a} + \sqrt{b} )( \sqrt{a} - \sqrt{b} ) = a - b \\ \\ \star \: \: \sf( \sqrt{a} \pm \sqrt{b} ) {}^{2} = {a}^{2} \pm2 \sqrt{ab} + b \\ \\ \star \: \: \sf{ (a + \sqrt{b})(a - \sqrt{b} ) = {a}^{2} - b } \end{array}}$

Coming back to the question again. Converting mixed fraction to proper fraction.

$\longrightarrow \sf{\quad {\sqrt{\dfrac{(36 \times 1 + 13)}{36}} }}$

Using the BODMAS rule, simplify further.

$\longrightarrow \sf{\quad {\sqrt{\dfrac{(36 + 13)}{36}} }}$

Performing the addition in the numerator of the fraction under square root.

$\longrightarrow \sf{\quad {\sqrt{\dfrac{49}{36}} }}$

Now, as it is known to us that √(a/b) is √a/√b. So,

$\longrightarrow \sf{\quad {\dfrac{\sqrt{49}}{\sqrt{36}} }}$

• Square root of 49 is 7.
• Square root of 36 is 6.

$\longrightarrow \quad \underline{\boxed{ \dfrac{\pmb{\frak{7}} }{\pmb{\frak{6}}} }}$

Therefore, the required answer is 7/6.