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3 years ago

Please help me with this question.

Mathematics

1 answer:

AleksAgata [21]3 years ago

5 0

Answer:

Step-by-step explanation:

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2. Which pole (north or south) of a compass magnet is attracted to Earth's magnetic north<br> pole?

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3 years ago

If √3 = 1.732, then √[(√3-1)/(√3+1)] is equal to

adelina 88 [10]

Step-by-step explanation:

<h3><u>Given Question :-</u></h3>

$\sf \: \sqrt{3} = 1.732, \: then \: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} }$

$\red{\large\underline{\sf{Solution-}}}$

Given expression is

$\rm :\longmapsto\: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} }$

<em>On rationalizing the denominator, we get </em>

$\rm \: = \: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \dfrac{ \sqrt{3} - 1}{ \sqrt{3} - 1} }$

$\rm \: = \: \sqrt{\dfrac{ {( \sqrt{3} - 1)}^{2} }{( \sqrt{3} + 1)( \sqrt{3} - 1)} }$

$\boxed{ \tt \: (x - y)(x + y) = {x}^{2} - {y}^{2} \: }$

<em>So, using this, we get </em>

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{ {( \sqrt{3})}^{2} - {(1)}^{2} } }$

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{ 3 - 1} }$

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{2} }$

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{2} } \times \dfrac{ \sqrt{2} }{ \sqrt{2} }$

$\rm \: = \: \dfrac{(1.732 - 1) \sqrt{2} }{2}$

$\rm \: = \: \dfrac{0.732 \times \sqrt{2} }{2}$

$\rm \: = \: 0.366 \sqrt{2}$

Hence,

$\rm :\longmapsto\: \boxed{ \rm{ \: \: \: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} } = 0.366 \sqrt{2} \: \: \: }}$

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<h2>More Identities to know :- </h2>

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)² = (a - b)² + 4ab

(a - b)² = (a + b)² - 4ab

(a + b)² + (a - b)² = 2(a² + b²)

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - b³ - 3ab(a - b)

3 0

3 years ago

Please help me with this question.​

Please help me with this question.