Radicals are among the challenging concepts in maths.

With this video below you can learn one of them and reach to the solution.

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Radicals are among the challenging concepts in maths.

With this video below you can learn one of them and reach to the solution.

Evaluate 13 x 369 + 331 x 13.

= 13 x 369 + 331 x 13.

= 13 x (369 + 331) factoring out the common number

= 13 x 700

= 9100 [after multiplying 16 and 7 and adding two zeros on
the answer]

Hence 13 x 369 + 331 x 13= 9100

Evaluate 127 x 516 + 484 x 127.

Find the sum of the 1st ten
terms of the geometrical progression 2+6+18+54+…….

G_{1} = 2, r=3, n=10

S_{n} = G_{1}(r^{n}-1)/r-1

S_{10} = 2(3^{10}-1)/3-1

S_{10} = ^{1}~~2~~(3^{10}-1)/~~2~~_{1}

S_{10 }= (3^{10}-1)

S_{10} = 59049 - 1

S_{10} = 59048

Hence the sum of the 1st
seven terms is 19682.

Find the sum of the 1st eight
terms of the geometrical progression 3+9+27+81+…..

If │4x – 7 │= 15; Find
x

±(4x – 11 )= 17

4x -11= 15 OR
–(4x-11) = 15

4x – 11 = 15
OR -4x+11=15

4x = 15 + 11 OR
-4x= 15-11

4
4 -4
-4

x = ^{13}/2
OR x = -1

If │2x – 7 │= 25; Find
x

If F(x) = log_{2}x,
Find F(32)

F(x) = log_{2}x

F(32) = log_{2}(32)

F(32) = log_{2}32^{-1}

F(32) = log_{2}(2^{5})^{-1}

F(32) = log_{2}2^{(5}
^{x} ^{-1)}

F(32) = log_{2}2^{-5}

F(32) = -5log_{2}2

F(32) = -5 x 1

F(32) = -5

If F(x) = log_{2}x,
Find F(512)

Factorize 625x^{2 }- 9y^{2}

We use difference of two squares a^{2} – b^{2} = (a - b)(a + b)

625x^{2}- 9y^{2}
= 25^{2}x^{2}^{ }- 3^{2}y^{2}

=
(25x)^{2}^{ }- (3y)^{2}

=
(25x - 3y)( 25x + 3y)

Factorize 225c^{2}- 36d^{2}

Find
a linear function f(x) with gradient -10 which is such that f(7)=16.

m=-10,
points = [7,16] and [x, f(x)]

m
= y_{2}-y_{1}/x_{2}-x_{1}

-10
= f(x) – 16/x-7

f(x)-16=-10(x-7)
[after cross multiply]

f(x)-16=-10x+70

f(x)=-10x+70+16

f(x)=-10x+86

Give
out a linear function f(x) with gradient 6 and f(8)=-4

Evaluate Log_{2}18
+ Log_{2}8 - Log_{2}9

= Log_{2}18
+ Log_{2}8 - Log_{2}9

= Log_{2}(18
x 8 ÷ 9)

= Log_{2}16

= Log_{2}2^{4}

= 4Log_{2}2

= 4 x 1 [since Log_{2}2=1]

Evaluate Log_{2}28
+ Log_{2}16 - Log_{2}7

The 1st term of arithmetic progression
is 37 and the common difference is 40. Find the nth term

A_{1}=37, d= 40, n=?

A_{n} =A1 + (n-1) d

A_{n}=37 + (n-1)40

A_{n}=37 + 40n -40

A_{n}=40n + 37-40

A_{n}=40n – 3

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