Surds help (1 Viewer)

[davidbarnes]

Ok, got an exam tomorrow, so am just revising. I'm confused with the following surd equations, and would appreiate some help and a good expanation of how to solve for these.

(3 root7)^3

(root5 + 7)^2

(root7 - root11)(root7 + root11)

2 root3 (4 root3 + 5)

Also some indices

(4x10^3)x(2x10^5)x(7x10^-4)

(8x10^-2)^3

and (6x10^3)^2

Any quick help would be great.

 

[vulgarfraction]

(a \sqrtb)^3 = a^3 * b^1.5

(\sqrta + b)^2 = a + b^2 + 2\sqrta *b

(\sqrta - \sqrtb)(\sqrta + \sqrtb) = a-b

Just know your rules and practise applying them.

 

[pLuvia]

1. Take it this way
3³*(rt{7})²*rt{7}

2. What's (rt{5}+7)(rt{5}+7), simply using multiplication

3. Take this one as the difference between two squares
i.e. rt{7}*rt{7}+rt{7}*rt{11}-rt{11}*rt{7}-rt{11}*rt{11}
=7-11
=-4

4. 2*4&(rt{3})²+2*5*rt{3x5}

5. 4x2x7x10^3+5+(-4) (Remember the laws of indices)

6. 8³x10^-2x3

7. Similiarly like 6

 

[jyu]

Ok, got an exam tomorrow, so am just revising. I'm confused with the following surd equations, and would appreiate some help and a good expanation of how to solve for these.

(3 root7)^3
(root5 + 7)^2
(root7 - root11)(root7 + root11)
2 root3 (4 root3 + 5)

Also some indices

(4x10^3)x(2x10^5)x(7x10^-4)
(8x10^-2)^3
and (6x10^3)^2
Any quick help would be great.

(3 root7)^3=3^3*(rt7)^3=27*7rt7=189rt7

(root5 + 7)^2=(rt5)^2+2*rt5*7+7^2=5+14*rt5+49=54+14*rt5

(root7 - root11)(root7 + root11)=(rt7)^2-(rt11)^2=7-11=-4

2 root3 (4 root3 + 5)=(2rt3)(4rt3)+(2rt3)*5=24+10rt3

Also some indices

(4x10^3)x(2x10^5)x(7x10^-4)=4*2*7*10^(3+5-4)=56*10^4=5.6*10^5

(8x10^-2)^3=(8^3)(10^-2)^3=512*10^-6=5.12*10^-4

and (6x10^3)^2=6^2*(10^3)^2=36*10^6=3.6*10^7

 

[davidbarnes]

Thanks for the help guys, it gives me a better understanding, espically on the indice laws.

 

[Affinity]

(a \sqrtb)^3 = a^3 * b^1.5

(\sqrta + b)^2 = a + b^2 + 2\sqrta *b

(\sqrta - \sqrtb)(\sqrta + \sqrtb) = a-b

Just know your rules and practise applying them.

Don't have TeX support yet and \sqrtb is not even correct LaTeX