expand and simplify where possible (5+√3)(5-√3)?

Question

I would be exstremly gratful if someone could help me with this quesion

Answer 1

use the identity

(x+a)(x-a) = x^2 - a^2

here, we let x =5 and a = sqrt of 3

this gives

(5+ sqrt3)(5 - sqrt 3)

5^2 -(sqrt3)^2 =25 -3 =22 as required

Answer 2

(5+√3)(5-√3)
= 25 - 5√3 + 5√3 - 3
= 22

Answer 3

25-3 = 22

Answer 4

You have to multiply the brackets together to expand them. You do this by essentially multiplying everything in one set of brackets by everything in the other set of brackets.
You must do this systematically, so first you multiply the 5 in the first brackets by the 5 in the second brackets, giving you 25. Then you multiply the 5 in the first brackets by the -√3 in the second brackets, giving you -5√3. Then you do the same with the +√3 in the first brackets - multiply it by the 5, then the -√3 in the second brackets.

This gives you:

25 + (-5√3) + 5√3 + ((+√3)x(-√3))


Then you need to simplify it:

25 is simple enough.
(-5√3) + 5√3 is 0, obviously.
(+√3)x(-√3) is just 3, but as one of the roots is minus, it's a minus 3.

So you're left with:

25 - 3

= 22


(am I right?)

Answer 5

method1
(5+√3)(5-√3) .......multiply
u get,
5*5-5√3+5√3-(√3*√3)...... solving
25-3 ......{as 5*5=25, and 5√3+5√3=0 and (√3*√3)=3}
22........ is the answer

method 2
(5+√3)(5-√3) can b simplified to the formula

(a+b)(a-b)=a^2-b^2

according to the formula the values of a and be will b as follows
a=5 and b =√3
solving we get
=5^2-√3^2
=25-3
=22 is the answer

Answer 6

=5^2-(√3)^2+5√3-5√3=25-3+0=22

basically you use the formula (a+b)(a-b)=a^2-b^2. Here, a=5, b=√3. so, we have 5^2-(√3)^2=25-3=22

Answer 7

(5+^3)(5-^3)=25+5^3-5^3-^9=25-3=22

Answer 8

(5+3^1/2)(5-3^1/2)=5^2-(3^1/2)^2
=25-3=22

Answer 9

okay start off with five tiems five which is 25, then it is minus 3 because -square root of three times +square root of three is -3 and 25-2=22

Answer 10

(5+sqroot3)(5-sqroot3)
= 25 +5(sqroot3) -5(sqroot3) -3
=25 - 3

=22