Question

Find the prime Factorization of 4320​

Answer 1

Step-by-step explanation:

Answer:

\frac{cos45°}{sec30+cosec60} =\frac{\sqrt{6}}{8}

sec30+cosec60

cos45°

=

8

6

Explanation:

______________________

we know that,

i) cos45° = 1/√2

ii) sec30° = 2/√3

iii ) cosec30° = 2/√3

______________________

Now ,

Value of

\frac{cos45°}{sec30+cosec60}

sec30+cosec60

cos45°

=\frac{\frac{1}{\sqrt{2}}}{\frac{2}{\sqrt{3}}+\frac{2}{\sqrt{3}}}=

3

2

+

3

2

2

1

=\frac{\frac{1}{\sqrt{2}}}{\frac{4}{\sqrt{3}}}=

3

4

2

1

= \frac{\sqrt{3}}{4\sqrt{2}}=

4

2

3

/*Rationalising the denominator, we get

=\frac{\sqrt{3}\times \sqrt{2}}{4\sqrt{2}\times\sqrt{2}}=

4

2

×

2

3

×

2

= \frac{\sqrt{6}}{8}=

8

6

Therefore,

\frac{cos45°}{sec30+cosec60} =\frac{\sqrt{6}}{8}

sec30+cosec60

cos45°

=

8

6

•••

Answer 2

Step-by-step explanation:

$\huge\underline\mathfrak{\green{Answer :-} }\:$.. Hello Dear!!!!

Here's your answer...

The given number is 4320

first,we have to do prime factorization

4320 = 2*2*2*2*2*3*3*3*5

4320 = 2^3 * 2^2 * 3^3 * 5

Here,

The power of 3 is 3

but the power of remaining 2 and 5 is not 3

The power of one 2 is 3....but the power of other 2 is 2

so...to become a perfect cube...the power should be 3

so...it should it multiplied with 2

The power of 5 is 1

It should be 3

so...we have to multiply two 5's

so...5*5 is 25

so...totally..

we have to multiply one 2 and two 5's

2*5*5

50

50 should be multiplied with 4320 to become perfect cube....

________________________________________________

HOPE THIS HELPS YOU....