Rationalize The Numerator

This video explains how to rationalize the numerator and the denominator.
Square Roots and Cube Roots: • Square Roots and Cube ...
Simplifying Radical Expressions:
• Simplifying Radicals
Multiplying Radical Expressions:
• Multiplying Radical Ex...
Adding & Subtracting Radicals:
• Adding and Subtracting...
Simplifying Cube Root Expressions:
• How To Simplify Cube R...
__________________________________
Rationalizing The Denominator:
• Rationalize The Denomi...
Multiplying Radicals With Different Indices:
• Multiplying Radical Ex...
How To Solve Radical Equations:
• Solving Radical Equations
Solving Equations With Cube Roots:
• Solving Equations With...
Solving Complex Radical Equations:
• How To Solve Complex R...
____________________________________
How To Graph Radical Functions:
• How To Graph Radical F...
Domain of Radical Functions:
• How To Find The Domain...
How To Graph Cube Root Functions:
• Graphing Cube Root Fun...
Radical Expressions - Test Review:
• Simplifying Radical Ex...
____________________________________
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Just a simple tip for y'all: when you have to multiply the numerator with same numericals but different signs, use this formulae -> (a+b).(a-b) = a²-b² because when you solve it, you end up in this form. For instance, ({√x+2} -3).({√x+2} +3) where {√x+2} is 'a' and 3 is 'b' so a²= x+2 (as roots get cancelled by squaring it) and b²= 9 and a²-b²=x+2-9 => *x-7* but it only applies when the a's and b's are same with different signs in it. Can ask me doubts :)

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it's a^2 - b^2, this is the *difference in squares* rule

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1:00 or you could use the identity (a+b)(a-b)=a^2-b^2 I find this identity very crucial in some questions

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A motor operating at 240v draws 10A while lifting a 2T block upward at a constant speed of 2.5m/s . Find (i) the horsepower rating (ii) the efficiency

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We can simply use the identity: a² - b² = ( a + b ) ( a - b) , after writing the conjugate

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How about the rationalizing the numerator with the same indices? Is this the same method of rationalizing numerator?

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I'm not nitpicking or anything but you can also simply use the formula of (a-b)(a+b) = a²-b²

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Shouldn't you have multiplied across the denominator at the 2:32 mark? Resulting it in the answer being 4/ 12 + 4 radical 5. I guess it wouldn't matter too much considering it results in the same answer 3 - radical 5/ 4. Mathway proves this.