INDICES & SURDS - The Mistake Fragment part 2

By Mr Johari

Identify the mistakes shown below and post your corrections.
For the correction identify the correct rules.

Find the algebra mistake: 
1.       mistake
2.      mistake
3.       mistake

4.      Find the algebra mistake: 

5.     Find the algebra mistake: 


  1. 1) Error in usage of the law of indices (When multiplying indices, exponents have to be added, not multiplied)

    2) Error in order of operations: In 10(1.3)^t, the multiplier 10 is multiplying 1.3^t, not just 1.3.

    3) Error in usage of Laws of indices (Laws of indices do not apply to addition)

    4) Error in manipulation of square root (square roots must be multiplied by itself, not just added, to make the expression rational)

    5) Careless error (Square root applies to the entire expression (x-1+h) and also (x-1), it is not possible to remove the square roots from only certain numbers immediately.)

  2. 1. When multiplying indices, indexes should be added, not multiplied.
    2. In 10(1.3)^t, 10 is being multiplied with 1.3^t, the index cannot be excluded, then put back in after calculation.
    3. Indexes cannot be added during addition of indices, the equation has to be factorised.
    4. The square root is multiplied by each other instead of added.
    5. Square root is applied to the whole equation, cannot be separated into just a square root of x.

  3. 1) When indices are multiplied they should be added.

    2) The exponent t must be added to 1.3 first, before multiplying by 10.

    3) Exponent cannot be added during addition, it can only be so when multiplying.

    4) √2x+1 multiplied by itself will give you 2x+1, addition of two equal square root does not apply.

    5) Square root applies to h also, it should be √h/h, not h/h.

  4. 1) When the terms are multiplied, the power has to be added, not multiplied.

    2) You must solve the bracket first, thus solve (1.3)^t then multiply the answer by 10.

    3) You can only add / subtract the powers if it is multiplied / divided respectively.

    4) You can only get that by multiplying, but in this case the answer should be 2(√2x+1).

    5) Square root is for all the terms, you cannot just put it for x.

  5. 1) No mistake
    2) Multiplying (1.3)^t by 10 ≠ (13)^t. Cannot just multiply 1.3 alone, have to multiply it after solving 't' and solving 13^t.
    3) Exponents cannot be added or multiplied when the equations are being added or subtracted. Only works with multiplication and division
    4) Can only get 2x+1 when (√2x+1)^2. In this case, its (√2x+1) + (√2x+1). Therefore (√2x+1) + (√2x+1) ≠ 2x+1
    5) Square root applies for all terms in the bracket, not just for x.