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
<u>1</u><u>1</u><u> </u><u>|</u><u> </u><u>1</u><u>3</u><u>3</u><u>1</u>
<u>1</u><u>1</u><u> </u><u>|</u><u> </u><u>1</u><u>2</u><u>1</u>
<u>1</u><u>1</u><u> </u><u>|</u><u> </u><u>1</u><u>1</u>
<u>|</u><u> </u><u>1</u><u>.</u>
Prime factorization of 1331 = <u>11 * 11 * 11</u>
³√(1331)
= ³√(<u>11 * 11 * 11</u>)
= 11
⇛³√(1331) = 11
Now,
Prime factorization of 5832
<u>2</u><u> </u><u>|</u><u> </u><u>5</u><u>8</u><u>3</u><u>2</u>
<u>2</u><u> </u><u>|</u><u> </u><u>2</u><u>9</u><u>1</u><u>6</u>
<u>2</u><u> </u><u>|</u><u> </u><u>1</u><u>4</u><u>5</u><u>8</u>
<u>3</u><u> </u><u>|</u><u> </u><u>7</u><u>2</u><u>9</u>
<u>3</u><u> </u><u>|</u><u> </u><u>2</u><u>4</u><u>3</u>
<u>3</u><u> </u><u>|</u><u> </u><u>8</u><u>1</u>
<u>3</u><u> </u><u>|</u><u> </u><u>2</u><u>7</u>
<u>3</u><u> </u><u>|</u><u> </u><u>9</u>
<u>3</u><u> </u><u>|</u><u> </u><u>3</u>
<u>|</u><u> </u><u>1</u><u>.</u>
Prime factorization of 5832 = <u>2*2*2</u> * <u>3*3*3</u> * <u>3*3*3</u>
Hence, ³√(5832)
= ³√(<u>2*2*2</u> * <u>3*3*3</u> * <u>3*3*3</u>)
= 2 * 3 * 3
= 6 * 3
= 18
⇛³√(5832) = 18
Therefore,
{(³√5832)/(³√1331)}
= 18/11
= {1(7/11)
<u>Answer:</u> Hence, the simplified form of ³√{4(508/1331)} is {1(7/11)}.
Please let me know if you have any other questions.
