How to Solve Surd Equations

In this video I show you how to solve equations involving surds. Surd equations have a square root in them and the method we use to solve these is to isolate the square root and then square both sides. This may need to be done a number of times depending on how many surds are in the equation.

Credits:
Kevin MacLeod: Carefree

[bottomtext]

Dont you just love it when your textbook only gives 2 types of examples and the questions come in 20 different question formats?

[leefordtanaka]

You know he's confident when he has a marker😂

[thando.gxothelwa]

What do you do when the second equation is equal to 0 instead of 1

[gundooscarmugumo]

Wow you explained it better than my teacher my GOD bless you ❤❤❤

[الفقيرالوضيع]

Pls sir what of surdic simultaneous equation

[ALADEOLUWARANTI]

Pls how can I solve the one that that we lead, e to quadratic equation.

[DODDREAMS]

Help me this math (r+5square root (r+8)=16

[leothunders]

Can u explain what "twice the product means?"

[SindisiweSithole-epdc]

Thanks a lot it such an amazing to learn hear❤

[zerotwo]

Thank you sir❤. I dont know math 123 also ... but need to come 😔

[annabelle]

I don't understand in the 2nd option to resolve the 2nd equation why (2√x-1)^2 is 4(x-1) and not (2√x-1).(2√x-1) which would be 4+2√x-1+2√x-1+x-1? Sorry this may be obvious!

[nadiaelhaj]

Just want to ask of how two came in the mid of one plus the root of x-1

[aivkhairulamirin]

For √(2-7x) + 2x=0
I got the answer
x=0.25 or x=-2

When I substitute x=-2 into the equation, the answer is 0.

However,
When I substitute x=0.25 into the equation, the answer is 1 not 0.

Why does it happen?🤔

[makuachukwujoel]

Sir am from Nigeria, I. Need any assistance to this question, 2√3*+4+*=36

[grrYT]

It doesn't make sense to me.. the second equation

[jan-willemreens]

... Alternative method to solve the 2nd equation SQRT(X + 4) - SQRT(X - 1) = 1 [ Let T = SQRT(X + 4) + SQRT(X - 1), the so-called Conjugate ... ] ... Multiply LHS and RHS of the given equation by the Conjugate T ... [ SQRT(X + 4) - SQRT(X - 1) ] * [ SQRT(X + 4) + SQRT(X - 1) ] = 1 * T [ Apply the Difference of 2 squares on the LHS: (A - B)(A + B) = A^2 - B^2 ] ... [ SQRT(X + 4) ]^2 - [ SQRT(X - 1) ]^2 = T .... X + 4 - (X - 1) = T .... T = 5 .... so now we have 2 equations: Eq. (a) SQRT(X + 4) - SQRT(X - 1) = 1 and Eq. (b) SQRT(X + 4) + SQRT(X - 1) = 5 ... Apply addition of Eq. (a) + Eq. (b) : 2 * SQRT(X + 4) = 6 ... SQRT(X + 4) = 3 .... X + 4 = 9 ... X = 5 ... NEVER FORGET TO CHECK YOUR CANDIDATE SOLUTION IN THE ORIGINAL EQUATION BEFORE VALIDATING ... X = 5 satisfies the original equation ( 3 - 2 = 1 ) and therefore S = { 5 } ... thank you for your math efforts, Jan-W

[akanjiwasiuabiodun]

Can't you solve the x+4=2√x-1 +x by not eliminating the two x . Is it also good solving straight away without eliminating the x before squaring the 4=2√x-1

[jacquelinemaisela]

thank you for this video and can you please also help out with functions(because I only understood this after you explained it...maybe it'll work on the others too)

[jacquelinecrowie]

why don't u use 2 to multiple with the 4(x-1) like