The BEST Way to Simplify Radical Math Problem FAST | You Should Try!

The BEST Way to Simplify Radical Math Problem FAST | You Should Try!

Lets dive into an exciting algebra challenge that tackles a radical simplification to test problem-solving skills. This problem is perfect for those looking to sharpen their algebraic techniques and expand their understanding of radicals. Join me as we explore this intriguing puzzle and break down the solution step by step. Whether you're preparing for a competition or just love a math challenge, this video is for you!

📌 Topics Covered:

Radical simplification
Algebraic manipulations
Problem-solving techniques
Algebraic identities
Math Olympiad preparation
How to de-nest radicals

🔢 What You'll Learn:

Key strategies for simplifying complex expressions
Tips and tricks to approach difficult simplification problems
Step-by-step walkthrough of the solution

🧠 Challenge Yourself:

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[jiangchuYT]

The first part is great. But the a^5 part, why not just use binomial theorem to expand it?
(\sqrt{18}+1)^5
=324\sqrt{18}+5\cdot 324
=1801+509\sqrt{18}
=1801+1527\sqrt{2}

[abhimanyubhattacharyya]

Kindly say when E= x^5, already mentioned then why once again E= a^5 is required ?

[gregevgeni]

3 + √8 = √2 ^2 + 1 + 2 √2 • 1 = ( 1+√2 )^2,
13 + 6√(1 + √2)^2 = 13 + 6(1 +√2) =
= 19 + 6√2 = 18 + 1 + 2 • 3√2
= (3√2)^2 + 1 + 2 •1• 3√2 = (1 + 3√2)^2.
So √ (13 + 6√(3 +√8))^5 =
=( √(1 + 3√2)^2 )^5 = ( 1 + 3√2)^5.
Let 1 + 3√2 = x => x^2 = 17 + 2 x .
x^5 = (x^2)(x^2)x = x •(17 + 2 x)^2 =
= x • (289 + 68 x + 4 x^2)
= x • [ 289 + 68 x + 4( 17 + 2 x) ]
= x • (357 + 76 x) = 357 x + 76 x^2
= 357 x + 76( 17 + 2 x)
= 1292 + 509 x = 1292 + 509( 1 + 3√2)
= 1801 + 1527√2 ..

[Shobhamaths]

E=1801+1527√2;
√(3+√8) =√2+1;
√(13+6(√2+1)) ;
√((19+6√2) ^5) ;√(1+3√2) ^5
Let x=1+3√2;x^2=17+2x
(x^2)^2=289+4x^2+68x
x^5=(289+4x^2+68x) *x
Simplify u get x^5=1801+1527√2👍

[gyogyir]

I can confirm that the " 1801+1527^2 " solution is correct