Question

please answer this....

Answer 1

Find the irrational numbers between 4and5

Answer 2

$<font color = "red"><b>Heya mate. (^_-). Solution below.</font color>$
====================================

$<u><font color = "pink">★ Answer 1 -</u></font color>$

♦ (2x + 3y)²


♠ Using identity - (a + b)² = a² + b² + 2ab,


→→→ (2x + 3y)²

= [ (2x)² + (3y)² + (2 × 2x × 3y)]

= [ 4x² + 9y² + 12xy]

= 4x² + 9y² + 12xy.. $<font color = "pink"><u>Answer !!</font color></u>$
==============================

$<u><font color = "blue">★ Answer 2 - </font color>$

♦ (1092)²

= (1000 + 92)²


♠ Using identity - (a + b)² = a² + b² + 2ab,


→→→ (1000 + 92)²

= [(1000)² + (92)² + (2 × 1000 × 92)]

= [1000000 + 8464 + 184000]

= 11,92,464.. $<font color = "blue"><u>Answer !!</font color></u>$
==============================

$<u><font color = "orange">★ Answer 3 -</font color></u>$

♠ Q. - What must be multiplied by 288 to make it a perfect cube?



♠ Ans. -

♦ Firstly, we find the prime factors of 288.


2 | 288
__|____
2 | 144
__|____
2 | 72
__|____
2 | 36
__|____
2 | 18
__|____
3 | 9
__|____
3 | 3
__|____
1 | 1


•°• 288 = 2 × 2 × 2 × 2 × 2 × 3 × 3

=> 288 = 2³ × 2² × 3²



♦ Now, we know that, a perfect cube is a number which is the third power of a number.

•°• 288 can be a perfect cube if it's prime factors are in cube, i.e., it should be 2³ × 2³ × 3³


So, 288 should be multiplied by one 2 and one 3 for becoming a perfect cube.

•°• 288 should be multiplied by 2 × 3 = 6 for becoming a perfect cube.. $<font color = "orange"><u>Answer !!</u></font color>$


♦ The number will become = 288 × 6 = 1728, which is a cube of (2 × 2 × 3) = 12.
====================================

$<marquee><font color = "green">Thank you ^_^ .$