Question

Give answers of the following
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Answer 1

1. Compare the numbers:

$\dfrac{ - 7}{9} , \: \dfrac{ - 8}{11}$

Let's take L.C.M to make the denominator same then we will compare and find which one is greater then other.

Taking L.C.M of 9 and 11 we get

9 | 9 - 11

11 | 1 - 11

| 1 - 1

9 × 11 = 99

So now to make denominator same we will multiply 9 with 11 and 11 with 9 to get 99 as denominator in both.

$- \dfrac{ 7 \times 11}{9 \times 11} = \dfrac{77}{99}$

Remember we will multiply 11 in both numerator and denominator because if we will multiply only in numerator then sense will be altered, you didn't need to change the question here when we multiply in both it gets cancel.

Another:-

$- \dfrac{ 8 \times 9}{11 \times 9} = \dfrac{72}{99}$

Now compare:

$\dfrac{77}{99} > \dfrac{72}{99}$

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2.) Find the cube root of - 13824

$\sqrt[3]{ - 13824}$

$= - \sqrt[3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3}$

Now pairing...

Here we have to make 3 pairs and rewrite them as single, As:

$= - (2 \times 2 \times 2 \times 3)$

$= - 24$

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