1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Assoli18 [71]
3 years ago
13

Rationalise the denominator of:1/(√3 + √5 - √2)​

Mathematics
1 answer:
Paul [167]3 years ago
6 0

Step-by-step explanation:

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

Given expression is

\rm :\longmapsto\:\dfrac{1}{ \sqrt{3}  +  \sqrt{5}  -  \sqrt{2} }

can be re-arranged as

\rm :\longmapsto\:\dfrac{1}{ \sqrt{3}   -   \sqrt{2}   +  \sqrt{5} }

\rm \:  =  \: \dfrac{1}{( \sqrt{3}  -  \sqrt{2} ) +  \sqrt{5} }

On rationalizing the denominator, we get

\rm \:  =  \: \dfrac{1}{( \sqrt{3}  -  \sqrt{2} ) +  \sqrt{5} }  \times \dfrac{( \sqrt{3}  -  \sqrt{2} ) -  \sqrt{5} }{( \sqrt{3}  -  \sqrt{2} ) -  \sqrt{5} }

We know,

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

So, using this, we get

\rm \:  =  \: \dfrac{ \sqrt{3} -  \sqrt{2}   -  \sqrt{5} }{ {( \sqrt{3}  -  \sqrt{2} )}^{2}  -  {( \sqrt{5}) }^{2} }

\rm \:  =  \: \dfrac{ \sqrt{3} -  \sqrt{2}   -  \sqrt{5} }{3 + 2 - 2 \sqrt{6}   - 5}

\rm \:  =  \: \dfrac{ \sqrt{3} -  \sqrt{2}   -  \sqrt{5} }{5 - 2 \sqrt{6}   - 5}

\rm \:  =  \: \dfrac{ \sqrt{3} -  \sqrt{2}   -  \sqrt{5} }{ - 2 \sqrt{6}}

\rm \:  =  \: \dfrac{ - ( -  \sqrt{3} +  \sqrt{2}  + \sqrt{5}) }{ - 2 \sqrt{6}}

\rm \:  =  \: \dfrac{-  \sqrt{3} +  \sqrt{2}  + \sqrt{5}}{2 \sqrt{6}}

On rationalizing the denominator, we get

\rm \:  =  \: \dfrac{-  \sqrt{3} +  \sqrt{2}  + \sqrt{5}}{2 \sqrt{6}}  \times \dfrac{ \sqrt{6} }{ \sqrt{6} }

\rm \:  =  \: \dfrac{-  \sqrt{18} +  \sqrt{12}  + \sqrt{30}}{2  \times 6}

\rm \:  =  \: \dfrac{-  \sqrt{3 \times 3 \times 2} +  \sqrt{2 \times 2 \times 3}  + \sqrt{30}}{12}

\rm \:  =  \: \dfrac{-  3\sqrt{2} + 2 \sqrt{3}   + \sqrt{30}}{12}

Hence,

\boxed{\tt{ \rm \dfrac{1}{ \sqrt{3}  +  \sqrt{5}  -  \sqrt{2} } =\dfrac{-  \sqrt{3 \times 3 \times 2} +  \sqrt{2 \times 2 \times 3}  + \sqrt{30}}{12}}}

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

<h3><u>More Identities to </u><u>know:</u></h3>

\purple{\boxed{\tt{  {(x  -  y)}^{2} =  {x}^{2} - 2xy +  {y}^{2}}}}

\purple{\boxed{\tt{  {(x   +   y)}^{2} =  {x}^{2} + 2xy +  {y}^{2}}}}

\purple{\boxed{\tt{  {(x   +   y)}^{3} =  {x}^{3} + 3xy(x + y) +  {y}^{3}}}}

\purple{\boxed{\tt{  {(x - y)}^{3} =  {x}^{3} - 3xy(x  -  y) -  {y}^{3}}}}

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

\pink{\boxed{\tt{  {(x + y)}^{2}  -  {(x - y)}^{2} = 4xy}}}

You might be interested in
The price of a toy usually costing £50 to £65 work out the percentage increase FAST!!
VLD [36.1K]

Answer:

50 * 1.3 = 65

130% increase

6 0
2 years ago
Read 2 more answers
Muiltiply 8x^2(x^2+2xy-6y^2) simplify your answer
stepladder [879]

The answer would be 8x^4 + 16x^3y - 48x^2y^2

In order to find this, multiply 8x^2 by each term individually.

8x^2 * x^2 = 8x^4

8x^2 * 2xy = 16 x^3y

8x^2 * -6y^2 = -48x^2y^2

Now you can put them all in a row.

8x^4 + 16x^3y - 48x^2y^2

3 0
3 years ago
Fernando bought a jacket for 185 and sold it for 1 1/2 what he paid. Marisol spent 1/5 as much as Fernando on the same jacket bu
avanturin [10]

Answer:

Marisol made $138.75 on the sale of the jacket

Step-by-step explanation:

First we are told that Fernando bought a jacket for $185, and sold it for 1 1/12 what he paid.

Therefore, 1 1/2 of 185;

= 1.5 × 185 = $277.5

Therefore, Fernando sold the Jacket for $277.5

Next, we are told that:

Marisol spent 1/5 as much as Fernando on the same jacket

This means that Marisol spent 1/5 of $185 on the jacket

= 1/5 × 185 = 0.2 × 185 = $37

Therefore, Marisol spent $37 to buy the same jacket

Next, Marisol sold the jacket for 1/2 as much as Fernando. Since Fernando sold the Jacket for $277.5, Marisol sold the jacket for 1/2 of 277.5, and this is calculated as:

1/2 of 277.5 = 0.5 × 277.5 = 138.75

Therefore, Marisol made $138.75 on the sale of the jacket.

6 0
3 years ago
Construct a truth table for the statement: (p v q) v (~p ^ q) -&gt; q
Gnom [1K]

Step-by-step explanation:

We have the following statement (p\lor q)\lor(\lnot p \land q) \rightarrow q

A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

The simple statements from the statement given are:

\lnot p, p\lor q, \lnot p \land q, and (p\lor q)\lor(\lnot p \land q)

This is the truth table.

8 0
3 years ago
Corey spent 25% of his savings on a printer at Louie’s Electronics.
KengaRu [80]
Let c represent the original amount that this guy had saved up.

He spent 25% of this amount, or 0.25c, on the printer. 

To progress further, we have to know how much the printer cost.

Supposing that the printer cost $100 (which we do not know as a fact), this would be equal to 0.25c.

Thus, his savings originally amounted to c = $100/0.25 = $400.
7 0
2 years ago
Other questions:
  • Given: ∆ABC, m∠C = 90° m∠BAC = 2m∠ABC BC = 24, AL −∠ bisector Find: AL
    8·1 answer
  • Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get
    15·1 answer
  • Solve each equation. I don't know this
    10·1 answer
  • Jernel has to figure out the area of her square garage. she knows that one side of the garage is equal to the length of her rabb
    14·1 answer
  • Solve for:<br><br><img src="https://tex.z-dn.net/?f=x%5E%7B2%7D%20%20%2B%205x%20%3D%201" id="TexFormula1" title="x^{2} + 5x = 1
    10·1 answer
  • Please help me with this. i don't understand it.
    7·2 answers
  • Here is the image I need help with
    10·1 answer
  • Please help a friend
    15·1 answer
  • I will give branliest to the first person to answer!
    5·1 answer
  • Find the LCM of 6 and 8 and list the multiples <br>​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!