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Why is it important to always factor the radicand first when simplifying radicals?
Wiki User
∙ 8y ago
The question is based on the premise that It is not possible to simplify a radical without first factorising it. That is simply not true. Beginners may find it a useful step but that does not make it "important to always factor".
Simplifying radicals entails removing square factors of the radicand from under the radical. This can be done without factoring first.
Wiki User
∙ 8y ago
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Can the radicand be negative when the index is even?
Given that the radicand is part of the question, not part of the answer, you can make the radicand whatever you want it to be. However, in any given root sum, for example, sqrt(-4), if the index is even, such as it is in a square root sum, the answer will always be positive. If the index is odd, and the radicand is negative, the answer will also be negative.
How can you simplify fraction?
To simplify a fraction, you find a number that can be divided by the fraction you are simplifying. sometimes this does not always work and the fraction can not be simplified.
How important or real is this world to the soul that is returning to Brahman?
Not at all important. Can always get back on the ride again later.
What is the important fact to remember when drawing an isometric drawing?
Always remember the turtles
What must be the same before two radicals can be multiplied or divided?
The radicals must have the same indexes.Examples when radicals have index of 2.√3√7 = √(3*7) = √21√2√6 = √(2*6) = √12 = √(4*3) = √4√3 = 2√3We decided that i2 = -1, and i = √-1, to be able to find the square root of any negative radicand, which is not a real number.For example,√-4 = √(-1*4) = √-1√4 = 2i.√-45 = √-1√45 = i√(9*5) = i√9√5 = 3√5 iAlso, we allow ourselves to multiply the radicals of index 2, even though one or both of the radicals are negative.√-5√6 = = √(-5*6) = √-30 = i√30. But I do prefer to work in this way:√-5√6 = = √-1√5√6 = = i√(5*6) = i√30. This work will eliminate the common mistake that students always do when they multiply radicals of index 2 with both negative radicands.For example,√-2√-3 = √(-2*-3) = √6 (wrong, a positive real number!)√-2√-3 = (√-1√2)(√-1√3) = (i)(i)√(2*3) = i2√6 = -√6.Examples of division:√10/√2 = √(10/2) = √5√-15/√3 = (√-1√15)/√3 = i√(15/3) = i√5√21/√-7 = √21/(√-1√7) = (1/i)√(21/7) = (1/i)√3 but this result is not a representative of an imaginary number, as we decided it to be. So what to do in order to manipulate the result and write it as a proper imaginary number?Let 1 = -(-1) = -(i2), then I will have (1/i)√3 = (-i2/i)√3 = -i√3, the right answer.Conclusion: 1/i = -i.√-35/√-5 = (√-1√35)/(√-1√5) = (i/i)(√35/5) = √7, the right work.Even though, √-35/√-5 = (√(-35/-5) = √(35/5) = √7, it is wrong to work in that way.So we solved the problem of finding the square roots of negative numbers, by using the imaginary number i, and we also called it a complex number, and so we built a new set of numbers, the set of complex numbers. Actually, all numbers are invention of our mind, even though I would prefer not to say it for the number 1.
Can the radicand be negative when the index is even?
Given that the radicand is part of the question, not part of the answer, you can make the radicand whatever you want it to be. However, in any given root sum, for example, sqrt(-4), if the index is even, such as it is in a square root sum, the answer will always be positive. If the index is odd, and the radicand is negative, the answer will also be negative.
When simplifying an expression you a always b sometimes c never perform operations inside grouping symbols first?
A
How can you simplify fraction?
To simplify a fraction, you find a number that can be divided by the fraction you are simplifying. sometimes this does not always work and the fraction can not be simplified.
What is sixty percent as a fraction?
60/100 is the most direct representation. Simplifying down to 6/10 or 3/5. Percent means "per 100". So a percent is always that number divided by 100.
When simplifying an expression do you always perform operations inside grouping symbols first?
It's possible to perform other operations first. But if you try it, there's a muchbigger chance that you'll get all tangled up and your result will be wrong.
What does simplification mean?
I guess you mean "simplifying": Writing a term in a form that is deemed simpler (this is not always unique). For example, "4" is a simplification of "2+2", or "x^2" is a simplification of "(x-1)*(x+1)+1".
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It depends on the circumstances. It is not always important
Why initiator efficiency in any free radical polymerization is always low?
Initiator efficiency in free radical polymerization is typically low because not all initiator molecules generate active radicals that are capable of initiating polymerization reactions. This is due to side reactions such as termination or chain transfer processes that can reduce the number of active radicals available for polymerization. Additionally, some radicals may not efficiently propagate the polymerization due to their reactivity or stability.
What is the important thing in dealing with customers?
The customer is always, always, right!
Does the word important always have a positive connotation?
No. If you are self-important, that is a negative.
Why is it important to have an objective?
its important to have an objective because you always supposed have an question to answer
Why is it important to not be gay?
It's NOT important not to be gay. If a person is gay, then they are gay. What's important is to always be who you are.
