10th General Math Exercise 1.3 Question 3

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In the name of Allah, the most gracious, the most merciful.
In this video we are going to solve question number three of 10th class math, general group, exercise one point three. So, stay with us.
Question number three is? Rationalize the denominators of the following; and part one is, one over under root three plus, two.
Let see its solution.
Is equal to, we are taking question as it is. Next we will multiply and divide the conjugate of denominator,
And denominator is indicated in blue color, which is under root three plus two. Its conjugate will be under root three minus two. So, we have multiplied and divided with conjugate which is under root three minus two.
One is multiplied with under root three minus two. So, it remains same.
Here, we are going to apply formula given below, which is a. plus b. into, a. minus b. is equal to a. square minus, b. square. in our question a. is under root three and b. is two. So, by applying formula under root three whole square is written.
Minus, comes from formula as given below.
Now, look at formula below, we have to write b. square, our b. is two, so, we write two square.
Equal to, under root three minus two, come as it is.
Here, square and square root are cancelled, and only three will be left.
Minus comes as it is.
Here, two square is opened as shown in details below, write two, two times and multiply them. Two twos are four. So, we write four.
Equal to, under root three minus two, come as it is.
Three minus four is minus one.
Is equal to.
This minus is taken above.
Under root three minus two is written as it is.
Since under root three has no sign so it is positive. And when minus is multiplied with plus, remains minus. As shown in details minus plus is minus.
Under root three comes with it.
Here, minus minus is plus. As shown in details.
Two is written as it is.
Now, plus two comes first, because it is positive, so minus three comes after it.
Hence, this is our final answer.
Question number three is? Rationalize the denominators of the following; and part two is, one over four minus under root five.
Let see its solution.
Is equal to, we are taking question as it is. Next we will multiply and divide the conjugate of denominator,
And denominator is indicated in blue color, which is four minus, under root five. Its conjugate will be four plus under root five. So, we have multiplied and divided with conjugate which is four plus, under root five.
One is multiplied with four plus under root five. So, it remains same.
Here, we are going to apply formula given below, which is a. plus b. into, a. minus b. is equal to a. square minus, b. square. in our question a. is four and b. is under root five. So, by applying formula four square is written.
Minus, comes from formula as given below.
Now, look at formula below, we have to write b. square, our b. is under root five, so, we write under root five whole square.
Equal to, four plus under root five, come as it is.
Here, four square is opened as shown in details below, write four, two times and multiply them. four fours are sixteen. So, we write sixteen.
Minus comes as it is.
Here, square and square root are cancelled, and only five will be left.
Equal to, four plus, under root five, come as it is.
Sixteen minus five is eleven.
Hence, this is our final answer.
Question number three is? Rationalize the denominators of the following; and part three is, four under root three, divided by, under root seven plus, under root five.
Let see its solution.
Is equal to, we are taking question as it is. Next we will multiply and divide the conjugate of denominator,
And denominator is indicated in blue color, which is under root seven plus, under root five. Its conjugate will be under root seven minus, under root five. So, we have multiplied and divided with conjugate which is under root seven minus, under root five.
Four under root three is multiplied with under root seven minus, under root five. Becomes, four under root three into under root seven minus, under root five
Here, we are going to apply formula given below, which is a. plus b. into, a. minus b. is equal to a. square minus, b. square. in our question a. is under root seven and b. is under root five. So, by applying formula, under root seven whole square is written.
Minus, comes from formula as given below.
Now, look at formula below, we have to write b. square, our b. is under root five, so, we write under root five whole square.
Equal to, four under root three, into, under root seven minus, under root five, come as it is.
Here, square and square root are cancelled, and only seven will be left.
Minus comes as it is.
Here, square and square root are cancelled, and only five will be left. , smart thinker club