The expression "1 by root 2 root 3 root 5" refers to the product of several square roots of prime numbers. In this expression, the numerator is 1, and the denominator is the product of the square roots of the prime numbers 2, 3, and 5.



To simplify the expression "1 by root 2 root 3 root 5," we need to start by simplifying each of the square roots in the denominator.

Step 1: Simplify the square root of 2

To simplify the square root of 2, we can multiply both the numerator and the denominator by the square root of 2. This gives us:

1 by root 2 root 2 root 3 root 5

Now we can simplify the square root of 2 by multiplying the two square roots together:

1 by root (2 x 2) root 3 root 5

Simplifying further, we get:

1 by root 4 root 3 root 5

Step 2: Simplify the square root of 4

To simplify the square root of 4, we can simply replace it with the number 2:

1 by 2 root 3 root 5

Step 3: Simplify the remaining square roots

Finally, we can multiply all the square roots together to get the simplified expression:

1/(2 x 3 x 5)

Step 4: Simplify the expression

Multiplying the denominator gives us:

1/30

Therefore, the expression "1 by root 2 root 3 root 5" is equivalent to 1/30.



In conclusion, the expression "1 by root 2 root 3 root 5" can be simplified to 1/30. This expression is useful in some mathematical calculations, especially in fields such as physics and engineering.