Hey! So as stupid as it sounds, I really don't understand radicals sometimes, so I'd really appreciate some help! In the following question can someone explain to me how they get that answer? I get the first step in solving the problem, but I really don't understand how they get THAT answer from that...Thanks!
Problem: (√2/2) (√3/2) + (√2/2) (1/2)
= (√2 √3 + √2)/4
Answer =(√2 (√3 + 1))/4
Problem: (√2/2) (√3/2) + (√2/2) (1/2)
= (√2 √3 + √2)/4
Answer =(√2 (√3 + 1))/4
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Actually, for this problem, you don't really need to know much about radicals. Let's go through your problem step by step.
√2 ... √3 ........... √2 .... 1
---- x ------ ... + ... ---- x -----
. 2 .... 2 .............. 2 .... 2
The first thing I'd do is use the distributive property of multiplication over addition, because we have a common factor of √2/2 in both terms. So, we get
√2 ...( √3 ..... 1 )
---- x (------ + ----)
. 2 ...(. 2 ...... 2 )
Now, we need to add the fractions √3/2 and 1/2. When you add fractions, you first write them with common denominators, and then you add the numerators. Here, we already have a common denominator of 2, so we can skip that step and go straight to
√2 ...( √3 + 1 )
---- x (------------)
. 2 ...(.... 2 ....)
Now, we're multiplying fractions. When we multiply fractions, we multiply the numerators, and then multiply the denominators. So, we get
√2 x ( √3 + 1 )
----------------------
..... 2 x 2
√2 x ( √3 + 1 )
----------------------
........ 4
Now, if you wanted to, you could redistribute the √2 into (√3 + 1). Using the distributive property, that would give you
√2 x √3 + √2 x 1
-------------------------
.......... 4
Now, you know that 1 times any number is always that number, so
√2 x √3 + √2
--------------------
........ 4
If you want to multiply √2 and √3, now you need to know something about radicals. The thing you need to know is, radicals are just a shorthand way of writing exponents. √2, the square root of 2, is the same thing as 2 raised to the power of 1/2, or 2^(1/2). (Similarly, a cube root is the same as raising to the power of 1/3.)
√2 ... √3 ........... √2 .... 1
---- x ------ ... + ... ---- x -----
. 2 .... 2 .............. 2 .... 2
The first thing I'd do is use the distributive property of multiplication over addition, because we have a common factor of √2/2 in both terms. So, we get
√2 ...( √3 ..... 1 )
---- x (------ + ----)
. 2 ...(. 2 ...... 2 )
Now, we need to add the fractions √3/2 and 1/2. When you add fractions, you first write them with common denominators, and then you add the numerators. Here, we already have a common denominator of 2, so we can skip that step and go straight to
√2 ...( √3 + 1 )
---- x (------------)
. 2 ...(.... 2 ....)
Now, we're multiplying fractions. When we multiply fractions, we multiply the numerators, and then multiply the denominators. So, we get
√2 x ( √3 + 1 )
----------------------
..... 2 x 2
√2 x ( √3 + 1 )
----------------------
........ 4
Now, if you wanted to, you could redistribute the √2 into (√3 + 1). Using the distributive property, that would give you
√2 x √3 + √2 x 1
-------------------------
.......... 4
Now, you know that 1 times any number is always that number, so
√2 x √3 + √2
--------------------
........ 4
If you want to multiply √2 and √3, now you need to know something about radicals. The thing you need to know is, radicals are just a shorthand way of writing exponents. √2, the square root of 2, is the same thing as 2 raised to the power of 1/2, or 2^(1/2). (Similarly, a cube root is the same as raising to the power of 1/3.)
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