Nice Algebra Square Root Simplification Problem

Added: 2026-06-08

[00:00:00]Hello everyone. So let's solve this maths square root problem which is <unk>x + <unk>2x +<unk> 3x is equal to 6. We have to find the value of x. So let's start with the solution.

[00:00:19]So write here root x plus here 2x is there. We can separate this as from this formula which is roo<unk> of a b is equal to<unk> of a * roo<unk> of b.

[00:00:35]So we can separate this as <unk>2 *<unk>x plus same here roo<unk>3 * <unk>x is = 6. Now take roo<unk>x as common rootx.

[00:00:53]So what we get here? what left? So this divide by this which is 1 plus this divide by this this will get cancel here comes <unk>2 plus this / this <unk>3 is equal to 6.

[00:01:15]Now divide both side by 1 + <unk>2 + <unk>3.

[00:01:29]Same here 1 + <unk>2 + <unk>3.

[00:01:34]So this will get cancel.

[00:01:37]So here we get square root of x = 6 over 1 + <unk>2 + <unk>3.

[00:01:49]Then next multiply this numerator and denominator which is 1 + <unk>2 - <unk>3.

[00:02:01]Then same denominator 1 + <unk>2 - <unk>3.

[00:02:09]So here square<unk> x is equal to 6 1 + <unk>2 - <unk>3.

[00:02:27]Now here use the formula. This is a plus and this is b a + b and a minus b. a + b a minus b is equal to a² - b².

[00:02:43]So here comes 1 + <unk>2² - <unk>3² So<unk>x = 6 1 + <unk>2 - <unk>3 over. Now here use the formula a + b square which is a² + 2 b + b². So here we get 1 square + 2<unk>2 + <unk>2² - this will cancel here comes 3.

[00:03:34]Next <unk>x = 6 1 + <unk>2 - <unk>3 over now this will get cancel here comes 1 + 2<unk>2 + 2 - 3 <unk>x is equal to 6 1 + <unk>2 - <unk>3 / 2<unk>2.

[00:04:17]Now we'll cancel this 2 3's are 6.

[00:04:21]So<unk>x = 3 1 + <unk>2 - <unk>3 / <unk>2.

[00:04:32]Now taking squaring on both side.

[00:04:38]So here this will get cancel.

[00:04:45]So x = 3² 1 + <unk>2 - <unk>3² over <unk>2².

[00:05:01]So x = 9 1 + <unk>2 - <unk>3 the whole square or this will get cancel here comes 2.

[00:05:16]Now here <unk>2 value is 1.41 and <unk>3 1.73.

[00:05:26]Put the value here. So we get x = 9 bracket 1 + 1.41 - 1.73 bracket close 2. So x = 9.

[00:05:47]Add this here comes 2.41 - 1.73² over 2.

[00:05:57]Now x = 9 bracket 0.68 the whole square / 2.

[00:06:07]So x = 9 0.68 * 0.68 which is 0.46 / 2. So x is equal to multiply this we get 4.16 over 2. So here we get the value of x which is 2.08.