1. Mathematics
  2. Can someone please help with

Can someone please help with this math question:)


Can someone please help with this math question:)

kimmy6973 kimmy6973    3   14.02.2022 03:20    10

Answers
dakotagorski05 dakotagorski05  14.02.2022 03:20

Solution:

The rationalisation factor for \frac{1}{ a - \sqrt{b} } is a + \sqrt{b}

So, let us apply it here.

\frac{1}{5 - \sqrt{2} }

The rationalising factor for 5 - √2 is 5 + √2.

Therefore, multiplying and dividing by 5 + √2, we have

= \frac{1}{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } \\ = \frac{5 + \sqrt{2} }{(5 - \sqrt{2})(5 + \sqrt{2} ) } \\ = \frac{5 + \sqrt{2} }{ {(5)}^{2} - ( \sqrt{2})^{2} } \\ = \frac{5 + \sqrt{2} }{25 - 2} \\ = \frac{5 + \sqrt{2} }{23}

\frac{5 + \sqrt{2} }{23}

Hope you could understand.

If you have any query, feel free to ask.

SHOW ANSWERS
bankskry bankskry  14.02.2022 03:20

\frac{5+\sqrt{2} }{23}

Step-by-step explanation:

To rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 5 - \sqrt{2} is 5 + \sqrt{2} , then

= \frac{1(5+\sqrt{2}) }{(5-\sqrt{2})(5+\sqrt{2}) } ← expand denominator using aFOIL

= \frac{5+\sqrt{2} }{25-2}

= \frac{5+\sqrt{2} }{23}

SHOW ANSWERS
SEND
Another questions on Mathematics
preciousharrington13 preciousharrington13  01.07.2021 19:40
Add (1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2) For each term in the second polynomial, enter the letter showing where that term should be placed to add the polynomials...
grenades5027 grenades5027  17.10.2020 05:01
-1.25 x 77.5 multiply integers....
fiorentinologan4 fiorentinologan4  26.05.2020 21:01
What is the total area, in square centimeters, to be painted blue....
azelyanoel azelyanoel  14.04.2021 20:30
Game 1 2 3 4. 5 6 7 8 Points Scored by Preston 8 12 10 9 13 12 15 9 What is the mean absolute deviation for the number of points Preston scored?...
allanarayos5597 allanarayos5597  04.01.2021 21:30
Please determine x....
milkshakegrande101 milkshakegrande101  05.10.2020 14:01
How does the author best create suspense in this excerpt? The captain is described as tranquil and unafraid, which shows that he is violent. Descriptive shaving details...
hollie62 hollie62  05.10.2020 14:01
Mary sews at a rate of 60 inches per hour. How many feet does she sew in a minute? a 0.003 rounded to the nearest thousandth b 0.083 rounded to the nearest thousandth...
josh200508 josh200508  05.10.2020 14:01
Part D Complete the table to find the rule for the translation, the coordinates of triangle A′B′C′, and the coordinates of the translated image, triangle A″B″C″....
nickthequick nickthequick  06.11.2019 00:31
Match the percentage with the equal decimal or fraction a)25% b)250% c)2500% d).25% e)2.5% 1)1/4 2)25 3)1/400 4)1/40 5)5/2...
bludragonfly33 bludragonfly33  23.02.2021 04:10
DOG or 1 pie O A. 3 x 1 / 2 = 2 3 3 O B. 4 x š = 4 x š = ☆ or 1 pies O C. 4x also 10 colo or 2 pies O D. 4 x ş 12 3 or 4 pies​...

Top Questions