Step-by-step explanation:
<h3><u>Given</u><u>:</u><u>-</u></h3>
(√3+√2)/(√3-√2)
<h3><u>To </u><u>find</u><u>:</u><u>-</u></h3>
<u>Rationalised</u><u> form</u><u> </u><u>=</u><u> </u><u>?</u>
<h3><u>Solution</u><u>:</u><u>-</u></h3>
We have,
(√3+√2)/(√3-√2)
The denominator = √3-√2
The Rationalising factor of √3-√2 is √3+√2
On Rationalising the denominator then
=>[(√3+√2)/(√3-√2)]×[(√3+√2)/(√3+√2)]
=>[(√3+√2)(√3+√2)]×[(√3-√2)(√3+√2)]
=>(√3+√2)²/[(√3-√2)(√3+√2)]
=> (√3+√2)²/[(√3)²-(√2)²]
Since (a+b)(a-b) = a²-b²
Where , a = √3 and b = √2
=> (√3+√2)²/(3-2)
=> (√3-√2)²/1
=> (√3+√2)²
=> (√3)²+2(√3)(√2)+(√2)²
Since , (a+b)² = a²+2ab+b²
Where , a = √3 and b = √2
=> 3+2√6+2
=> 5+2√6
<h3><u>Answer:-</u></h3>
The rationalised form of (√3+√2)/(√3-√2) is 3+2√6+2.
<h3>
<u>Used formulae:-</u></h3>
→ (a+b)² = a²+2ab+b²
→ (a-b)² = a²-2ab+b²
→ (a+b)(a-b) = a²-b²
→ The Rationalising factor of √a-√b is √a+√b
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Evaluate the expression 4(2x+y)-2y+z for x=-2, y=4 and z=-3

Before inserting the values of the variables, I recommend writing the equation in its simplest form.
First, use the distributive property and distribute 4:-
8x+4y-2y+z
Simplifying,
8x+2y+z
Now that the expression is in its simplest form, we can substitute the variables and simplify the expression.
First, write -2 in lieu of x:-
8(-2)+2y+z
-16+2y+z
Now, write 4 in lieu of y:-
-16+2(4)+z
-16+8+z
-8+z
Final step:-
write -3 in lieu of z:-
-8+(-3)
-8-3
-11
<h3>Good luck.</h3>
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What are your options for the questions.
Answer:
<h2>
w = -8</h2>
Step-by-step explanation:
Given the equation solved by Ernesto expressed as
, the extraneous solution obtained by Ernesto is shown below;

Hence, the extraneous solution that Ernesto obtained is w = -8
Answer:
6.42$
Step-by-step explanation:
6.00 divided by 100 equals 0.6 multiplied by 7 equals 0.42 so the sales tax is 0.42 cents and the total is 6.42$