Question

Simplify: 3√4 508/1331

Answer 1

Answer:

${\sqrt[3]{4 \dfrac{508}{1331}}}$ = $\dfrac{18}{11}$ or $1\dfrac{7}{11}$

Step-by-step explanation:

Solving this question by prime factorization method :

$\begin{gathered}\implies{\tt{\sqrt[3]{4 \dfrac{508}{1331}}}}\end{gathered}$

$\begin{gathered}\implies{\tt{\sqrt[3]{ \dfrac{(4 \times 1331) + 508}{1331}}}}\end{gathered}$

$\begin{gathered}\implies{\tt{\sqrt[3]{ \dfrac{(5324) + 508}{1331}}}}\end{gathered}$

$\begin{gathered}\implies{\tt{\sqrt[3]{ \dfrac{5324 + 508}{1331}}}}\end{gathered}$

$\begin{gathered}\implies{\tt{\sqrt[3]{ \dfrac{5832}{1331}}}}\end{gathered}$

Prime factorization of :

• 5832 = 2×2×2×3×3×3×3×3×3
• 1331 = 11×11×11

$\begin{gathered}{\implies{\small{\tt{\sqrt[3]{ \dfrac{2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3}{11 \times 11 \times 11}}}}}}\end{gathered}$

$\begin{gathered}{\implies{\small{\tt{\sqrt[3]{ \dfrac{ \underbrace{2 \times 2 \times 2} \times \underbrace{3 \times 3 \times 3} \times \underbrace{3 \times 3 \times 3}}{ \underbrace{11 \times 11 \times 11}}}}}}}\end{gathered}$

$\begin{gathered}{\implies{\tt{\dfrac{2 \times 3\times 3}{11}}}}\end{gathered}$

$\begin{gathered}{\implies{\tt{\dfrac{6\times 3}{11}}}}\end{gathered}$

$\begin{gathered}{\implies{\tt{\dfrac{18}{11}}}}\end{gathered}$

$\begin{gathered}{\implies{\tt{\underline{\underline{\red{1\dfrac{7}{11}}}}}}}\end{gathered}$

Hence, the answer is 18/11 or 1(7/11).

$\rule{300}{2.5}$

Answer 2

Answer:

The simplified form of ³√{4(508/1331)} is {1(7/11)}.

Step-by-step explanation:

Given that:

³√{4(508/1331)}

Let we first convert the mixed fraction to simplest fraction form.

= ³√{(1331*4+508)/1331}

= ³√{(5324 + 508)/1331}

= ³√(5832/1331)

Comparing the fraction with x√{(a/b)}, we get

a = 5832 , b = 1331 and x = 3

Using exponent rule x√{(a/b)} = {(x√a)/(x√b)}, we get

= {(³√5832)/(³√1331)}

Let now find the prime factorization of 5832 and 1331.

Prime factorization of 1331

11 | 1331

11 | 121

11 | 11

| 1.

Prime factorization of 1331 = 11 * 11 * 11

³√(1331)

= ³√(11 * 11 * 11)

= 11

⇛³√(1331) = 11

Now,

Prime factorization of 5832

2 | 5832

2 | 2916

2 | 1458

3 | 729

3 | 243

3 | 81

3 | 27

3 | 9

3 | 3

| 1.

Prime factorization of 5832 = 2*2*2 * 3*3*3 * 3*3*3

Hence, ³√(5832)

= ³√(2*2*2 * 3*3*3 * 3*3*3)

= 2 * 3 * 3

= 6 * 3

= 18

⇛³√(5832) = 18

Therefore,

{(³√5832)/(³√1331)}

= 18/11

= {1(7/11)

Answer: Hence, the simplified form of ³√{4(508/1331)} is {1(7/11)}.

Please let me know if you have any other questions.