Simplify \(\sqrt{98}\).
Answer (3)
When you're simplifying a square root that isn't a square number, the best idea is to find two multiples, one of which is a square number. 49 and 2 are multiples, and 49 is a square number, and this the makes it easier to simplify. This then becomes outside of the root (as this is simplified as far as possible), leaving root 2. Below is the method that shows how they are divided. 98 = 49 x 2 = 49 m u lt i pl i e d b y 2 = 7 2
Hope this helps :)
In this example, we are asked to simplify the square root of 98. First, notice that 98 is not a perfect square. This means that it's impossible to find a whole number times itself which equals 98. However, it's important to understand that the square root of 98 can still be simplified. We can simplify the square root of 98 by setting up a factor tree.
Looking at the image provided, you can notice that there is a pair of sevens in our factor tree. This means that 7 can come out of the radical. Notice that there is also a 2 in our factor tree that does not pair up. This means that the 2 stays inside the radical and this gives us 7 times the square root of 2.
Therefore, the square root of 98 simplifies to 7 root 2 or 2 7 .
To simplify 98 , we factor it into 2 × 49 , where 49 is a perfect square equal to 7 × 7 . This allows us to rewrite the square root as 7 2 . Thus, the simplified form is 7 2 .
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